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Solving Equation Worksheets

This segment has an endless collection of equation worksheets based on solving one-step, two-step and multi-step equations; rearranging literal equations, writing the equation of a line in various forms; graphing linear equation and more. High-school topics such as quadratic equation, absolute value equation and systems of equations are also featured here. Practice solving the equations by using the various download options available. A number of free printable worksheets are also up for grabs!

List of Equation Worksheets

Explore the equation worksheets in detail.

One-step equation worksheets

This set of worksheets requires students to solve one-step equations involving integers, fractions and decimals by performing addition, subtraction, multiplication or division operations. It also contains math riddles, finding the cost of the objects, translating the phrases into one-step equation and more.

Two-step equation worksheets

Click on the link to access exclusive worksheets on solving two-step equations that include integers, fractions and decimals. A number of MCQ's, equations in geometry, translating two-step equations and many more exercises are available for practice.

Multi-step equation worksheets

These worksheets require students to perform multiple steps to solve the equations. Use the knowledge gained in solving one-step and two-step equations to solve these multi-step equations. A number of application oriented problems based on geometrical shapes are also included here.

Equation word problems worksheets

Download and print this enormous collection of one-step, two-step and multi-step equation word problems that include integers, fractions, and decimals. MCQ worksheets form a perfect tool to examine a learner's perception on the topic.

Rearranging Equations worksheets

Literal equation worksheets help to hone the skills like rearranging the literal equations, rearrange and evaluate, word problems containing real-life applications and a lot more are included.

Equation of a line worksheets

Click here for worksheets on equation of a line. Write the equation of a line in standard form, two-point form, slope-intercept form and point-slope form. Download the complete set of worksheets on equation of a line that comprise worksheets on parallel and perpendicular lines as well.

Graphing linear equation worksheets

You are just a click away from a huge collection of worksheets on graphing linear equations. Plot the points and graph the line. Use the x values to complete the function tables and graph the line. The MCQ worksheets form a perfect tool to test student's knowledge on this topic.

Quadratic equation worksheets

Click on the link for an extensive set of worksheets on quadratic equations. Solve the quadratic equations by factoring, completing the square, quadratic formula or square root methods. Find the sum and product of the roots. Analyze the nature of the roots.

Absolute value equation worksheets

Use these worksheets to teach your students about the absolute value of integers. This module includes exercises like evaluating the absolute value expression at a particular value, input and output tables, graph the absolute value function and solve the various types of absolute value equation.

Systems of equations worksheets

Solve these systems of equations by elimination or substitution methods. The equations contain two or three variables. Equation with two variables represents straight lines, whereas equations with three variables represent a plane.

Sample Worksheets

Equation Word Problems

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Free Math Worksheets — Over 100k free practice problems on Khan Academy

Looking for free math worksheets.

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That’s because Khan Academy has over 100,000 free practice questions. And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun!

Just choose your grade level or topic to get access to 100% free practice questions:

Kindergarten, basic geometry, pre-algebra, algebra basics, high school geometry.

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Statistics and probability

High school statistics, ap®︎/college statistics, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra.

  • Addition and subtraction
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Worksheets for simplifying expressions

Worksheets for evaluating expressions with variables

Worksheets for writing expressions with variables from verbal expressions

Worksheets for linear inequalities

Key to Algebra workbook series

Key to Algebra Workbooks

Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system.

Practice makes perfect. Practice math at IXL.com

Free Math Worksheets by Math-Drills

Math-Drills.com includes over 70,000 free math worksheets that may be used to help students learn math. Our math worksheets are available on a broad range of topics including number sense, arithmetic, pre-algebra, geometry, measurement, money concepts and much more. There are two interactive math features: the math flash cards and dots math game.

Math-Drills.com was launched in 2005 with around 400 math worksheets. Since then, tens of thousands more math worksheets have been added. The website and content continues to be improved based on feedback and suggestions from our users and our own knowledge of effective math practices.

Most Math-Drills users are classroom teachers or parents. Classroom teachers use our math worksheets to assess student mastery of basic math facts, to give students extra math practice, to teach new math strategies, and to save precious planning time. Parents use our math worksheets to give their children extra math practice over school breaks and to enhance their math education. Home schools use our math worksheets in their programs to develop and strengthen math skills in their children.

Most Popular Free Math Worksheets this Week

Multiplying 2-Digit by 2-Digit Numbers

Supporting Student Learning with Free Math Worksheets by Math-Drills

Math-Drills believes that education should be accessible to all children despite their socioeconomic situation or any other factors. Since it began in 2005, all the math worksheets on Math-Drills have been free-to-use with students learning math. The Math-Drills website works well on any device and worksheets can be printed or used on a screen.

Math-Drills worksheets are also used in special education, adult education, tutoring, colleges, high schools, prisons and a variety of other situations. Special education teachers especially like that we break down math skills and provide large-print options. Adult learners appreciate the simple uncluttered format that our worksheets offer. Tutors use our math worksheets to reduce their costs and focus on student learning. High school, college and university educators sometimes need remedial resources for students to allow them to continue with more advanced topics.

Students who practice their math skills with our math worksheets over school breaks keep their math skills sharp for upcoming school terms. Because we provide answer keys, students are able to self-assess and use the immediate feedback provided by an answer key to analyze and correct errors in their work. Our interactive (fillable) math worksheets allow them to fill in their answers on the screen and save or print the results.

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Algebra Worksheets

Free worksheets with answer keys.

Enjoy these free printable sheets . Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

  • Distance Formula
  • Equation of Circle
  • Factor Trinomials Worksheet
  • Domain and Range
  • Mixed Problems on Writing Equations of Lines
  • Slope Intercept Form Worksheet
  • Standard Form Worksheet
  • Point Slope Worksheet
  • Write Equation of Line from the Slope and 1 Point
  • Write Equation of Line from Two Points
  • Equation of Line Parallel to Another Line and Through a Point
  • Equation of Line Perpendicular to Another Line and Through a Point
  • Slope of a Line
  • Perpendicular Bisector of Segment
  • Write Equation of Line Mixed Review
  • Word Problems
  • Multiplying Monomials Worksheet
  • Multiplying and Dividing Monomials Sheet
  • Adding and Subtracting Polynomials Worksheet
  • Multiplying Monomials with Polynomials Worksheet
  • Multiplying Binomials Worksheet
  • Multiplying Polynomials
  • Simplifying Polynomials
  • Factoring Trinomials
  • Operations with Polynomials Worksheet
  • Dividing Radicals
  • Simplify Radicals Worksheet
  • Adding Radicals
  • Mulitplying Radicals Worksheet
  • Radicals Review (Mixed review worksheet on radicals and square roots)
  • Solve Systems of Equations Graphically
  • Solve Systems of Equations by Elimination
  • Solve by Substitution
  • Solve Systems of Equations (Mixed review)
  • Activity on Systems of Equations (Create an advertisement for your favorite method to Solve Systems of Equations )
  • Real World Connections (Compare cell phone plans)
  • Scientific Notation
  • Operations with Scientific Notation

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Worksheets to Practice Solving Equations

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></center></p><h2>Worksheets to Practice Solving Equations</h2><p>Math Worksheets / Algebra Worksheets / Worksheets to Practice Solving Equations</p><p>Equations come in many forms and there is a lot to untangle. Students of all abilities are tasked with solving linear equations , systems of equations , quadratic equations , and more as part of their school curriculum. Luckily for them, our solving equations math worksheets with answers are here to help practice all types of equations through engaging practice. Solving linear equations and quadratic equations have never been easier with the help of our worksheets with answers .</p><h2>Printable Middle School and High School Equations Worksheets</h2><p>Solving equations takes a lot of practice as it involves being able to break down and make sense of all the different steps, terms, and variables.</p><p>Practicing, making mistakes, and learning from these mistakes is the only way that solving linear equations and quadratic equations becomes easier. Whether you’re looking for a math worksheet on solving linear equations or quadratic equations, a worksheet on solving equations in a geometric context, or a worksheet on solving systems of equations, we have a vast selection of worksheets for you that cover all levels of ability. All children learn in different ways, which is why we provide solving equations worksheets, as well as “I’m thinking of a number” worksheets.</p><h2>Equations Worksheets Can Help Students in the Real World</h2><p>When learning about equations for the first time, many students question how useful this information is in the real world. </p><p>What they often don’t realize is that we encounter equations in many aspects of our daily lives, and we can often use equations to solve real-world problems, such as how much paint to buy or what the price of an item will be after various discounts are applied. Learning about algebraic equations allows students to apply their knowledge in areas such as physics, chemistry, computer science, game development and more. Using equations worksheets is a great way for students to practice their algebra knowledge and help them along the way to becoming the next Steven Hawking or Steve Jobs.</p><h2>Help Students Learn How to Solve Equations with Practice Worksheets</h2><p>Kids learn best when they are interested in the subject, so try to find activities that make the topic of solving equations fun and entertaining. </p><p>There are many resources available on Cazoom Math that break down the steps for solving equations into understandable pieces and help keep students engaged in their math learning. Solving all types of equations requires critical thinking, recognizing patterns, and understanding the properties of operations. With regular practice, students’ problem-solving skills will begin to improve. Problem-solving abilities are valued not just for mathematical and scientific study, but this skill is also widely sought after by employers in a range of industries. Algebra may seem daunting now, but regularly practicing with equations worksheets can help students develop these skills for life.</p><h2>WHAT ARE ONE STEP EQUATIONS AND HOW TO SOLVE THEM?</h2><p>One step equation is an algebraic equation that you can easily solve with only one step. They are quite easy and quick to solve. It takes you only one step to solve and find the variable. </p><p>To solve a one step equation all you need to do is inverse the operation that is being performed on the variable.</p><p>Adding – subtracting</p><p>Multiplication – Dividing </p><p>It is quite simple because you have to follow only one rule. When solving a one step equation whatever you do on one side of the equation, you have to do the same thing to the other side as well. </p><h2>QUICK EXAMPLE: SOLVE THE X IN THE ONE STEP EQUATION</h2><p>x – 13 = 7</p><p>We need to get the x by itself on the left side of the equation and to do that we need to inverse and add 13 on both sides. Follow the next steps:</p><p>x – 13 + 13 = 7 + 13</p><h2>TWO STEP EQUATIONS AND HOW TO SOLVE THEM</h2><p>Quite similar to the one step equation, you need to solve the algebraic equation, and get the variable by itself with no numbers in front of it, by using two steps.  </p><h2>QUICK EXAMPLE: SOLVE THE X IN THE TWO STEP EQUATION</h2><p>5x + 3 = 28</p><p>5x + 3 – 3 = 28 – 3</p><p>Always check if the solution to the two step equation is right.</p><p>5×5 + 3 = 28</p><p>25 + 3 = 28</p><h2>GET 30 FREE MATH WORKSHEETS!</h2><p>Fill out the form below to get 30 FREE math worksheets.</p><ul><li>Home   |  </li><li>About   |  </li><li>Contact Us   |  </li><li>Privacy   |  </li><li>Copyright   |  </li><li>Shop   |  </li><li>🔍 Search Site</li><li>Kindergarten</li><li>All Generated Sheets</li><li>Place Value Generated Sheets</li><li>Addition Generated Sheets</li><li>Subtraction Generated Sheets</li><li>Multiplication Generated Sheets</li><li>Division Generated Sheets</li><li>Money Generated Sheets</li><li>Negative Numbers Generated Sheets</li><li>Fraction Generated Sheets</li><li>Place Value Zones</li><li>Number Bonds</li><li>Addition & Subtraction</li><li>Times Tables</li><li>Fraction & Percent Zones</li><li>All Calculators</li><li>Fraction Calculators</li><li>Percent calculators</li><li>Area & Volume Calculators</li><li>Age Calculator</li><li>Height Calculator</li><li>Roman Numeral Calculator</li><li>Coloring Pages</li><li>Fun Math Sheets</li><li>Math Puzzles</li><li>Mental Math Sheets</li><li>Online Times Tables</li><li>Online Addition & Subtraction</li><li>Math Grab Packs</li><li>All Math Quizzes</li><li>1st Grade Quizzes</li><li>2nd Grade Quizzes</li><li>3rd Grade Quizzes</li><li>4th Grade Quizzes</li><li>5th Grade Quizzes</li><li>6th Grade Math Quizzes</li><li>Place Value</li><li>Rounding Numbers</li><li>Comparing Numbers</li><li>Number Lines</li><li>Prime Numbers</li><li>Negative Numbers</li><li>Roman Numerals</li><li>Subtraction</li><li>Add & Subtract</li><li>Multiplication</li><li>Fraction Worksheets</li><li>Learning Fractions</li><li>Fraction Printables</li><li>Percent Worksheets & Help</li><li>All Geometry</li><li>2d Shapes Worksheets</li><li>3d Shapes Worksheets</li><li>Shape Properties</li><li>Geometry Cheat Sheets</li><li>Printable Shapes</li><li>Coordinates</li><li>Measurement</li><li>Math Conversion</li><li>Statistics Worksheets</li><li>Bar Graph Worksheets</li><li>Venn Diagrams</li><li>All Word Problems</li><li>Finding all possibilities</li><li>Logic Problems</li><li>Ratio Word Problems</li><li>All UK Maths Sheets</li><li>Year 1 Maths Worksheets</li><li>Year 2 Maths Worksheets</li><li>Year 3 Maths Worksheets</li><li>Year 4 Maths Worksheets</li><li>Year 5 Maths Worksheets</li><li>Year 6 Maths Worksheets</li><li>All AU Maths Sheets</li><li>Kindergarten Maths Australia</li><li>Year 1 Maths Australia</li><li>Year 2 Maths Australia</li><li>Year 3 Maths Australia</li><li>Year 4 Maths Australia</li><li>Year 5 Maths Australia</li><li>Meet the Sallies</li><li>Certificates</li></ul><h2>Basic Algebra Worksheets</h2><p>Welcome to the Math Salamanders' Basic Algebra Worksheets. Here you will find a range of algebra worksheets to help you learn about basic algebra, including generating and calculating algebraic expressions and solving simple problems.</p><p>For full functionality of this site it is necessary to enable JavaScript.</p><p>Here are the instructions how to enable JavaScript in your web browser .</p><p>Quicklinks to ...</p><h2>Basic Algebra Support</h2><p>Generate the Expression Worksheets</p><h2>Calculate the Expression Worksheets</h2><ul><li>Solve the Equations Worksheets</li><li>More recommended resources</li><li>Basic Algebra Online Quiz</li></ul><p>Want to gain a basic understanding of algebra?</p><p>Looking for some simple algebra worksheets?</p><p>Do you need a bank of useful algebra resources?</p><p>Look no further! The pages you need are below!</p><p>Here is our selection of basic algebra sheets to try.</p><p>We have split the worksheets up into 3 different sections:</p><ul><li>Generate the algebra - and write your own algebraic expressions;</li><li>Calculate the algebra - work out the value of different expressions;</li><li>Solve the algebra - find the value of the term in the equation.</li></ul><p>By splitting the algebra up into sections, you only need to concentrate on one aspect at a time!</p><p>Each question sheet comes with its own separate answer sheet.</p><p>Want to test yourself to see how well you have understood this skill?.</p><ul><li>Try our NEW quick quiz at the bottom of this page.</li></ul><p>What is an algebraic expression?</p><p>An expression is a mathematical statement where variables and operations are combined.</p><ul><li>2a + 5 is an expression involving the variable a</li><li>5(y 2 - 6) is another expression</li></ul><p>What is an algebraic equation?</p><p>An equation is where an algebraic expression is equal to something, which might be a number, or another algebraic expression.</p><ul><li>2a + 5 = 7 is an equation</li><li>5(y 2 - 6) = 3y + 8 is another equation</li></ul><p>How to Generate an Expression</p><p>When we are generating an expression, we are taking a rule and turning it into algebra.</p><ul><li>Subtract 6 from n could be written as n - 6.</li><li>Multiply d by 4 could be written as d x 4 or 4d.</li><li>Add 5 to p and then double the result is written as (p + 5) x 2 or 2(p + 5)</li></ul><p>How to Calculate an Expression</p><p>When we are calculating the value of an expression, we work out the value of the expression when we give a value to the variable.</p><ul><li>p + 5 has a value of 11 when p = 6 because 6 + 5 = 11</li><li>4(n - 2) has a value of 32 when n = 10 because 4 x (10 - 2) = 4 x 8 = 32</li><li>4(n - 2) has a value of -8 when n = 0 because 4 x (0 - 2) = 4 x (-2) = -8</li></ul><p>How to Solve a Simple Equation</p><p>When we are solving an equation, we are finding out the value(s) of the variable in the equation.</p><ul><li>If p + 5 = 9 then p = 4 because 4 + 5 = 9</li><li>then (n - 2) = 28 ÷ 4 = 7</li><li>if (n - 2) = 7 then n = 7 + 2 = 9</li><li>Answer: n = 9</li><li>means that 3f = 12</li><li>so f = 12 ÷ 3 = 4</li><li>Answer: f = 4</li></ul><h2>Basic Algebra Worksheets for kids</h2><ul><li>Generate the Expression 1</li><li>PDF version</li><li>Generate the Expression 2</li><li>Generate the Expression 3</li></ul><h2>Generate the Expression Word Problems</h2><ul><li>Algebra Word Problems 1</li><li>Algebra Word Problems 2</li><li>Algebra Word Problems 3</li><li>Algebra Word Problems 3 UK Version</li></ul><h2>Algebra Word Problems Walkthrough Video</h2><p>This short video walkthrough shows the problems from our Algebra Word Problems Worksheet 2 being solved and has been produced by the West Explains Best math channel.</p><p>If you would like some support in solving the problems on these sheets, please check out the video below!</p><p><center><iframe style=

  • Calculate the Expression 1
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Solve the Equation Worksheets

  • Solve the Equation 1
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Free Algebra Problem Solver

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  • 6th Grade Distributive Property Worksheets

The sheets on this page have been designed to factorize and expand a range of simple expressions using the distributive property..

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The sheets on this page have been specially designed for 6th graders and are a great introduction to expressions and equations.

Factorising Quadratic Equations

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  • Algebra Math Games

If you are looking for a fun printable algebra game to play then try out our algebra game page.

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PEMDAS Worksheets

The sheets in this section involve using parentheses and exponents in simple calculations.

There are also lots of worksheets designed to practice and learn about PEMDAS.

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  • PEMDAS Problems Worksheets 5th Grade
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Interactive Equality Explorer

This interactive equality explorer has been produced by PhET Interactive Simulations at the University of Colorado.

It is a useful tool for exploring different ideas including negative numbers and algebra equations and equality.

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You can then select your level of difficulty and start solving some algebraic equations by getting your variables onto one side of the equation and the numerical values on the other, and then multiplying or dividing the equation until you find the value of the required variable.

interactive equality explorer by PhET

  • Interactive Equality Explorer by PhET

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Unit 2: Solving equations & inequalities

About this unit, linear equations with variables on both sides.

  • Why we do the same thing to both sides: Variable on both sides (Opens a modal)
  • Intro to equations with variables on both sides (Opens a modal)
  • Equations with variables on both sides: 20-7x=6x-6 (Opens a modal)
  • Equation with variables on both sides: fractions (Opens a modal)
  • Equation with the variable in the denominator (Opens a modal)
  • Equations with variables on both sides Get 3 of 4 questions to level up!
  • Equations with variables on both sides: decimals & fractions Get 3 of 4 questions to level up!

Linear equations with parentheses

  • Equations with parentheses (Opens a modal)
  • Reasoning with linear equations (Opens a modal)
  • Multi-step equations review (Opens a modal)
  • Equations with parentheses Get 3 of 4 questions to level up!
  • Equations with parentheses: decimals & fractions Get 3 of 4 questions to level up!
  • Reasoning with linear equations Get 3 of 4 questions to level up!

Analyzing the number of solutions to linear equations

  • Number of solutions to equations (Opens a modal)
  • Worked example: number of solutions to equations (Opens a modal)
  • Creating an equation with no solutions (Opens a modal)
  • Creating an equation with infinitely many solutions (Opens a modal)
  • Number of solutions to equations Get 3 of 4 questions to level up!
  • Number of solutions to equations challenge Get 3 of 4 questions to level up!

Linear equations with unknown coefficients

  • Linear equations with unknown coefficients (Opens a modal)
  • Why is algebra important to learn? (Opens a modal)
  • Linear equations with unknown coefficients Get 3 of 4 questions to level up!

Multi-step inequalities

  • Inequalities with variables on both sides (Opens a modal)
  • Inequalities with variables on both sides (with parentheses) (Opens a modal)
  • Multi-step inequalities (Opens a modal)
  • Using inequalities to solve problems (Opens a modal)
  • Multi-step linear inequalities Get 3 of 4 questions to level up!
  • Using inequalities to solve problems Get 3 of 4 questions to level up!

Compound inequalities

  • Compound inequalities: OR (Opens a modal)
  • Compound inequalities: AND (Opens a modal)
  • A compound inequality with no solution (Opens a modal)
  • Double inequalities (Opens a modal)
  • Compound inequalities examples (Opens a modal)
  • Compound inequalities review (Opens a modal)
  • Solving equations & inequalities: FAQ (Opens a modal)
  • Compound inequalities Get 3 of 4 questions to level up!

Algebra Equations Worksheets

Algebra equations are the most basic concept of algebra that form the foundation and act as the building blocks of the concept. It is, because of that very reason, important to do a good amount of practice of questions on them. One might find a lot of resources online on Algebra equations but you have to smartly choose where to invest your time to get the most of it.

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Solving equations

Here you will learn about solving equations, including linear and quadratic algebraic equations, and how to solve them.

Students will first learn about solving equations in grade 8 as a part of expressions and equations, and again in high school as a part of reasoning with equations and inequalities.

What is solving an equation?

Solving equations is a step-by-step process to find the value of the variable. A variable is the unknown part of an equation, either on the left or right side of the equals sign. Sometimes, you need to solve multi-step equations which contain algebraic expressions.

To do this, you must use the order of operations, which is a systematic approach to equation solving. When you use the order of operations, you first solve any part of an equation located within parentheses. An equation is a mathematical expression that contains an equals sign.

For example,

\begin{aligned}y+6&=11\\\\ 3(x-3)&=12\\\\ \cfrac{2x+2}{4}&=\cfrac{x-3}{3}\\\\ 2x^{2}+3&x-2=0\end{aligned}

There are two sides to an equation, with the left side being equal to the right side. Equations will often involve algebra and contain unknowns, or variables, which you often represent with letters such as x or y.

You can solve simple equations and more complicated equations to work out the value of these unknowns. They could involve fractions, decimals or integers.

What is solving an equation?

Common Core State Standards

How does this relate to 8 th grade and high school math?

  • Grade 8 – Expressions and Equations (8.EE.C.7) Solve linear equations in one variable.
  • High school – Reasoning with Equations and Inequalities (HSA.REI.B.3) Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

[FREE] Math Equations Check for Understanding Quiz (Grade 6 to 8)

[FREE] Math Equations Check for Understanding Quiz (Grade 6 to 8)

Use this quiz to check your grade 6 to 8 students’ understanding of math equations. 10+ questions with answers covering a range of 6th, 7th and 8th grade math equations topics to identify areas of strength and support!

How to solve equations

In order to solve equations, you need to work out the value of the unknown variable by adding, subtracting, multiplying or dividing both sides of the equation by the same value.

  • Combine like terms .
  • Simplify the equation by using the opposite operation to both sides.
  • Isolate the variable on one side of the equation.

Solving equations examples

Example 1: solve equations involving like terms.

Solve for x.

Combine like terms.

Combine the q terms on the left side of the equation. To do this, subtract 4q from both sides.

The goal is to simplify the equation by combining like terms. Subtracting 4q from both sides helps achieve this.

After you combine like terms, you are left with q=9-4q.

2 Simplify the equation by using the opposite operation on both sides.

Add 4q to both sides to isolate q to one side of the equation.

The objective is to have all the q terms on one side. Adding 4q to both sides accomplishes this.

After you move the variable to one side of the equation, you are left with 5q=9.

3 Isolate the variable on one side of the equation.

Divide both sides of the equation by 5 to solve for q.

Dividing by 5 allows you to isolate q to one side of the equation in order to find the solution. After dividing both sides of the equation by 5, you are left with q=1 \cfrac{4}{5} \, .

Example 2: solve equations with variables on both sides

Combine the v terms on the same side of the equation. To do this, add 8v to both sides.

7v+8v=8-8v+8v

After combining like terms, you are left with the equation 15v=8.

Simplify the equation by using the opposite operation on both sides and isolate the variable to one side.

Divide both sides of the equation by 15 to solve for v. This step will isolate v to one side of the equation and allow you to solve.

15v \div 15=8 \div 15

The final solution to the equation 7v=8-8v is \cfrac{8}{15} \, .

Example 3: solve equations with the distributive property

Combine like terms by using the distributive property.

The 3 outside the parentheses needs to be multiplied by both terms inside the parentheses. This is called the distributive property.

\begin{aligned}& 3 \times c=3 c \\\\ & 3 \times(-5)=-15 \\\\ &3 c-15-4=2\end{aligned}

Once the 3 is distributed on the left side, rewrite the equation and combine like terms. In this case, the like terms are the constants on the left, –15 and –4. Subtract –4 from –15 to get –19.

Simplify the equation by using the opposite operation on both sides.

The goal is to isolate the variable, c, on one side of the equation. By adding 19 to both sides, you move the constant term to the other side.

\begin{aligned}& 3 c-19+19=2+19 \\\\ & 3 c=21\end{aligned}

Isolate the variable to one side of the equation.

To solve for c, you want to get c by itself.

Dividing both sides by 3 accomplishes this.

On the left side, \cfrac{3c}{3} simplifies to c, and on the right, \cfrac{21}{3} simplifies to 7.

The final solution is c=7.

As an additional step, you can plug 7 back into the original equation to check your work.

Example 4: solve linear equations

Combine like terms by simplifying.

Using steps to solve, you know that the goal is to isolate x to one side of the equation. In order to do this, you must begin by subtracting from both sides of the equation.

\begin{aligned} & 2x+5=15 \\\\ & 2x+5-5=15-5 \\\\ & 2x=10 \end{aligned}

Continue to simplify the equation by using the opposite operation on both sides.

Continuing with steps to solve, you must divide both sides of the equation by 2 to isolate x to one side.

\begin{aligned} & 2x \div 2=10 \div 2 \\\\ & x= 5 \end{aligned}

Isolate the variable to one side of the equation and check your work.

Plugging in 5 for x in the original equation and making sure both sides are equal is an easy way to check your work. If the equation is not equal, you must check your steps.

\begin{aligned}& 2(5)+5=15 \\\\ & 10+5=15 \\\\ & 15=15\end{aligned}

Example 5: solve equations by factoring

Solve the following equation by factoring.

Combine like terms by factoring the equation by grouping.

Multiply the coefficient of the quadratic term by the constant term.

2 x (-20) = -40

Look for two numbers that multiply to give you –40 and add up to the coefficient of 3. In this case, the numbers are 8 and –5 because 8 x -5=–40, and 8+–5=3.

Split the middle term using those two numbers, 8 and –5. Rewrite the middle term using the numbers 8 and –5.

2x^2+8x-5x-20=0

Group the terms in pairs and factor out the common factors.

2x^2+8x-5x-20=2x(x + 4)-5(x+4)=0

Now, you’ve factored the equation and are left with the following simpler equations 2x-5 and x+4.

This step relies on understanding the zero product property, which states that if two numbers multiply to give zero, then at least one of those numbers must equal zero.

Let’s relate this back to the factored equation (2x-5)(x+4)=0

Because of this property, either (2x-5)=0 or (x+4)=0

Isolate the variable for each equation and solve.

When solving these simpler equations, remember that you must apply each step to both sides of the equation to maintain balance.

\begin{aligned}& 2 x-5=0 \\\\ & 2 x-5+5=0+5 \\\\ & 2 x=5 \\\\ & 2 x \div 2=5 \div 2 \\\\ & x=\cfrac{5}{2} \end{aligned}

\begin{aligned}& x+4=0 \\\\ & x+4-4=0-4 \\\\ & x=-4\end{aligned}

The solution to this equation is x=\cfrac{5}{2} and x=-4.

Example 6: solve quadratic equations

Solve the following quadratic equation.

Combine like terms by factoring the quadratic equation when terms are isolated to one side.

To factorize a quadratic expression like this, you need to find two numbers that multiply to give -5 (the constant term) and add to give +2 (the coefficient of the x term).

The two numbers that satisfy this are -1 and +5.

So you can split the middle term 2x into -1x+5x: x^2-1x+5x-5-1x+5x

Now you can take out common factors x(x-1)+5(x-1).

And since you have a common factor of (x-1), you can simplify to (x+5)(x-1).

The numbers -1 and 5 allow you to split the middle term into two terms that give you common factors, allowing you to simplify into the form (x+5)(x-1).

Let’s relate this back to the factored equation (x+5)(x-1)=0.

Because of this property, either (x+5)=0 or (x-1)=0.

Now, you can solve the simple equations resulting from the zero product property.

\begin{aligned}& x+5=0 \\\\ & x+5-5=0-5 \\\\ & x=-5 \\\\\\ & x-1=0 \\\\ & x-1+1=0+1 \\\\ & x=1\end{aligned}

The solutions to this quadratic equation are x=1 and x=-5.

Teaching tips for solving equations

  • Use physical manipulatives like balance scales as a visual aid. Show how you need to keep both sides of the equation balanced, like a scale. Add or subtract the same thing from both sides to keep it balanced when solving. Use this method to practice various types of equations.
  • Emphasize the importance of undoing steps to isolate the variable. If you are solving for x and 3 is added to x, subtracting 3 undoes that step and isolates the variable x.
  • Relate equations to real-world, relevant examples for students. For example, word problems about tickets for sports games, cell phone plans, pizza parties, etc. can make the concepts click better.
  • Allow time for peer teaching and collaborative problem solving. Having students explain concepts to each other, work through examples on whiteboards, etc. reinforces the process and allows peers to ask clarifying questions. This type of scaffolding would be beneficial for all students, especially English-Language Learners. Provide supervision and feedback during the peer interactions.

Easy mistakes to make

  • Forgetting to distribute or combine like terms One common mistake is neglecting to distribute a number across parentheses or combine like terms before isolating the variable. This error can lead to an incorrect simplified form of the equation.
  • Misapplying the distributive property Incorrectly distributing a number across terms inside parentheses can result in errors. Students may forget to multiply each term within the parentheses by the distributing number, leading to an inaccurate equation.
  • Failing to perform the same operation on both sides It’s crucial to perform the same operation on both sides of the equation to maintain balance. Forgetting this can result in an imbalanced equation and incorrect solutions.
  • Making calculation errors Simple arithmetic mistakes, such as addition, subtraction, multiplication, or division errors, can occur during the solution process. Checking calculations is essential to avoid errors that may propagate through the steps.
  • Ignoring fractions or misapplying operations When fractions are involved, students may forget to multiply or divide by the common denominator to eliminate them. Misapplying operations on fractions can lead to incorrect solutions or complications in the final answer.

Related math equations lessons

  • Math equations
  • Rearranging equations
  • How to find the equation of a line
  • Solve equations with fractions
  • Linear equations
  • Writing linear equations
  • Substitution
  • Identity math
  • One step equation

Practice solving equations questions

1. Solve 4x-2=14.

GCSE Quiz False

Add 2 to both sides.

Divide both sides by 4.

2. Solve 3x-8=x+6.

Add 8 to both sides.

Subtract x from both sides.

Divide both sides by 2.

3. Solve 3(x+3)=2(x-2).

Expanding the parentheses.

Subtract 9 from both sides.

Subtract 2x from both sides.

4. Solve \cfrac{2 x+2}{3}=\cfrac{x-3}{2}.

Multiply by 6 (the lowest common denominator) and simplify.

Expand the parentheses.

Subtract 4 from both sides.

Subtract 3x from both sides.

5. Solve \cfrac{3 x^{2}}{2}=24.

Multiply both sides by 2.

Divide both sides by 3.

Square root both sides.

6. Solve by factoring:

Use factoring to find simpler equations.

Set each set of parentheses equal to zero and solve.

x=3 or x=10

Solving equations FAQs

The first step in solving a simple linear equation is to simplify both sides by combining like terms. This involves adding or subtracting terms to isolate the variable on one side of the equation.

Performing the same operation on both sides of the equation maintains the equality. This ensures that any change made to one side is also made to the other, keeping the equation balanced and preserving the solutions.

To handle variables on both sides of the equation, start by combining like terms on each side. Then, move all terms involving the variable to one side by adding or subtracting, and simplify to isolate the variable. Finally, perform any necessary operations to solve for the variable.

To deal with fractions in an equation, aim to eliminate them by multiplying both sides of the equation by the least common denominator. This helps simplify the equation and make it easier to isolate the variable. Afterward, proceed with the regular steps of solving the equation.

The next lessons are

  • Inequalities
  • Types of graph
  • Coordinate plane

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Algebra Equations Worksheets

Created: February 13, 2024

Last updated: February 13, 2024

In mathematics, an algebraic equation is a statement that sets two expressions equal. Variables, coefficients, and constants are the standard components of an algebraic equation. A simple algebraic equation looks something like p + 16 = 12. In the equation, p stands for 4.

What Are Algebraic Worksheets?

The algebraic operations—addition, subtraction, multiplication, division, raising to the power—are used to a collection of variables to build an equation, which states that two expressions are equal. With the algebra equations worksheets, kids learn to reason. The algebra 1 solving equations worksheets teach abstract thinking and strengthen these reasoning abilities. The main point is that variables, represented by symbols like x and y, may be utilized to fill in gaps in mathematical or real-world problems or to comprehend dynamic connections.

By learning to create and interpret visual representations of data, algebra 1 equations worksheets also aid pupils in visualizing intricate ideas and connections. Students can develop their brainpower and acquire new thinking methods by understanding abstract, dynamic, and complicated concepts.

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Importance of Algebra Worksheets 

When kids use the algebra equations worksheets PDF, they learn to organize their thoughts. They are better equipped to come up with rational answers when faced with complex or ever-changing problems. 

The worksheets also help kids prepare for the future. Students may benefit from developing their critical thinking and problem-solving abilities even if they do not major in math or science in college or if they do not choose a profession in those fields. Pre algebra equations worksheets introduce kids to many possibilities that can be explored using algebra.

Also, algebra is a must for high school seniors planning to attend university. The more advanced math and science courses needed to get into most universities build on algebraic concepts. So, kids need to understand the fundamental aspects of algebra before moving to motored complex ideas. With time, kids get familiar with higher-level math courses taken by high school pupils and also excel in college admission examinations like the SAT and ACT.

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.

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A multiply and dividing integers worksheets for graders help them to grasp the rationale behind these operations. Integer multiplication and division are foundational mathematical concepts that will stay with the learner as they progress through school. Free multiplying and dividing integers worksheets Using free multiplying and dividing integers worksheets can boost kids’ problem-solving abilities and […]

It’s common for kids to struggle with the addition of fractions. Helping your kids learn the fraction-related concepts requires using a suitable math resource. Adding fractions with like denominators worksheets are a tested approach to taking your kids from math learners to experts. Free Adding Fractions with the Same Denominator Worksheet The knowledge of how […]

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  1. Equation Worksheets

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    Algebra Equations Worksheets. In mathematics, an algebraic equation is a statement that sets two expressions equal. Variables, coefficients, and constants are the standard components of an algebraic equation. A simple algebraic equation looks something like p + 16 = 12. In the equation, p stands for 4.

  18. Free Printable Math Worksheets for Algebra 2

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    Balancing Equations First Grade - One Worksheet. Comparing Numbers - 2 Worksheets. Comparing Numbers - 1 Worksheet. Comparing Numbers - 1 Worksheet. Pan Balance Problems - Three Worksheets. Pan Balance Problems - Three Worksheets. Pan Balance Problems - Two Worksheets. Algebra - Solve for m - Solve the equation - 6 ...

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