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Two-Step Inequalities Worksheets

Ratchet up skills with our printable two step inequalities worksheets curated for students in grade 7, grade 8, and high school. It takes two steps to solve these inequalities that contain more than one operation. Undo addition or subtraction first followed by division or multiplication using inverse operations to isolate the variable. Transcend through easy, moderate and difficult levels and master solving and graphing two-step inequalities involving whole numbers, integers, decimals, and fractions like a pro. Tread just two steps, download and print and access our free two step inequalities worksheets!

Identifying Solutions to Two-Step Inequalities

Don't let the four options flummox your 7th grade students. Get them to follow a trial-and-error method by substituting each option in the inequality and solve it. Identify and circle the solutions that satisfy each inequality.

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Solving Two-Step Inequalities

The mantra is to get the variable isolated on one side by performing inverse operations on either side. First eliminate the constants, followed by coefficients and solve the two-step inequalities with a never-before ease.

Solving and Graphing Two-Step Inequalities

Ally solving with plotting with our printable two step inequalities worksheets and work toward your pursuit of finding and graphing the relative value on number lines with an open or closed circle and arrow mark indicating the solution range.

Spotting the Solutions in Interval Notations

Grow the skills of your students in grade 7 and grade 8 in solving two-step inequalities in meteoric proportions, as they steer clear through these two step inequalities pdfs finding the range of solutions from the four intervals given.

Solving Two-Step Inequalities | Fractions and Decimals

By turns interesting and challenging these printable two step inequalities worksheets with twin number types: fractions and decimals, your students are sure to hit new heights in solving these inequalities.

Finding Solutions and Graphing Two-Step Inequalities

With a hard to beat versatility, these solving and graphing two-step inequalities get students in 7th grade and 8th grade to solve the inequalities with fraction and decimal coefficients and constants in two-steps and graph them on a number line.

Identifying Solution Graphs

Identifying the correct solution graph for each two-step inequality is not beyond your ken. High school students solve the inequality by using the additive and multiplicative inverses to isolate the variable and identify the graph that best describes the solution.

Identifying Two-Step Inequality from the Number Line

Observe the number line keenly, identify the relative value, comprehend if the inequality is inclusive or strict from the open or closed circle, look at the direction of the ray to figure out the solution. Choose the two-step inequality whose solution this could possibly be.

Translating Inequality Phrases Worksheets

In this part of our two-step inequalities pdf worksheets, grade 7 and grade 8 students get adequate practice in setting up a two-step inequality by translating verbal descriptions of real-life scenarios. Watch out! You may have to use variables on both sides.

(12 Worksheets)

Related Worksheets

» One Step Inequalities

» Multi Step Inequalities

» Compound Inequalities

» Absolute Value Inequalities

» Two Step Equations

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Real World Algebra by Edward Zaccaro

Algebra is often taught abstractly with little or no emphasis on what algebra is or how it can be used to solve real problems. Just as English can be translated into other languages, word problems can be "translated" into the math language of algebra and easily solved. Real World Algebra explains this process in an easy to understand format using cartoons and drawings. This makes self-learning easy for both the student and any teacher who never did quite understand algebra. Includes chapters on algebra and money, algebra and geometry, algebra and physics, algebra and levers and many more. Designed for children in grades 4-9 with higher math ability and interest but could be used by older students and adults as well. Contains 22 chapters with instruction and problems at three levels of difficulty.

Representing and Solving Linear Inequalities: Worksheets with Answers

Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.

Mathster keyboard_arrow_up Back to Top

Mathster is a fantastic resource for creating online and paper-based assessments and homeworks. They have kindly allowed me to create 3 editable versions of each worksheet, complete with answers.

Corbett Maths keyboard_arrow_up Back to Top

Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. It really is one of the very best websites around.

Solving Linear Inequalities Worksheets with Solutions

Solving linear inequalities is a foundational skill that you will build throughout your studies of elementary and high school algebra. While it isn’t the hardest concept you will encounter in the entire class, there are a few tips and tricks you should get used to. And the best way to do that is by practicing! 

That’s why I put together this collection of solving linear inequalities worksheets! Let’s dig in so that you can master this important algebra concept!

What is a Linear Inequality?

A linear inequality is a type of statement in algebra that compares two linear equations. To make this comparison, we place an inequality symbol in between the two sides of the inequality. For example, \(x+1>2x-1\).

Take a moment to review this inequality symbol list:

• < (less than)
• > (greater than)
• ≤ (less than or equal to)
• ≥ (greater than or equal to)

Linear inequalities are similar to linear equations, however instead of an equals sign, a linear inequality contains one of the inequality symbols from the above list.

How to Solve a Linear Inequality

The steps that you take to solve a linear inequality are a very similar to those that you would take while  solving an algebraic equation . When solving linear inequalities, you often perform similar operations as you would when  solving linear equations . 

Just like in linear equations, you can add or subtract terms on both sides, and multiply or divide by constants on both sides. However, unlike solving linear equations, linear inequalities have one  very  important rule:

Remember: If you multiply or divide both sides of an inequality by a negative number, the inequality sign must be flipped! 

You will see some examples of this in the solving linear inequalities worksheets linked below!

Another important difference between solving a linear equation and solving a linear inequality is that the solution to a linear inequality will be the  set of all values  that make the inequality true (rather than just a  single value  that makes the equation true).

The solution to a linear inequality will tell you the places on the graph where one line is greater than or less than the other.

For example, consider the coordinate plane below that shows two lines in slope-intercept form. 

As you can see, the red line is above the green line as long as \(x<2\). After this, the green line is above the red line. So if we wanted to write the solution to \(x+1>2x-1\), we would say that the solution set is \(x<2\), or all x-values less than 2 (note that we do not include 2 in the solution set since that is the point where the lines are equal ).

Solving Algebraically

In order to solve \(x+1>2x-1\) algebraically, we will use the same algebra strategies that we use when solving linear equations. We will collect all x-terms on the left side of the equation, and all non-variable terms on the right side of the equation.

\begin{split} x+1&>2x-1 \\ \\ -x&>-2 \\ \\ x&<2 \end{split}

Since we had to divide both sides by -1, notice that we flipped the sign of the inequality symbol! Therefore, the solution to this inequality is x<2 (which we can confirm using the coordinate plane above).

Another way that we can represent this solution is on a number line . We draw a line to the left of 2 with a hollow circle at 2 to indicate that 2 is  not  part of our solution set. We would use a filled in dot to indicate a value that  is  part of the solution set.

There are many ways to solve linear inequalities and represent their solutions. In the math worksheets that follow below, you will focus mainly on solving algebraically and representing your answer on a number line!

One-Step Inequalities Math Worksheet

To get started, try the set of one-step inequalities in the worksheet linked below. These problems will help you become familiar with solving a linear equality algebraically, and representing the solution on a number line. 

I have created this worksheet in PDF format for your convenience. Remember to check the answer key provided to make sure that you understand the basics of solving linear inequalities.

Download the PDF worksheet by clicking below!

Multi-Step Inequalities Math Worksheet

Now that you have had some practice with solving one-step inequality problems, use the following worksheet to try your hand at some more complex linear inequality problems. This worksheet contains two-step inequalities as well as some more difficult multi-step linear inequality problems! 

This worksheet is also provided in PDF format for ease of access. Remember to check the answer key to confirm your understanding of solving more complex linear inequalities.

Practice Solving Linear Inequalities

Inequalities may seem scary at first because of the inequality symbol, but as you have seen, they are actually solved in a very similar way to linear equations.

Use the math worksheets linked above to practice getting comfortable with solving a variety of linear inequality problems. Like any math concept, the more you practice the more familiar the concept will start to feel.

I hope these solving linear inequalities worksheets have helped you practice your inequality solving skills, as well as representing the solution set on a number line!

Ready to start applying your skills? Check out this linear inequalities word problems worksheet !

Did you find these solving linear inequalities worksheets helpful? Share this post and subscribe to Math By The Pixel on YouTube for more helpful mathematics content!

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Graph Basic Inequalities on Number Lines (A)

Welcome to The Graph Basic Inequalities on Number Lines (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2014-12-08 and has been viewed 132 times this week and 899 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

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Mathematics is often regarded as a fundamental subject in education, providing essential skills and concepts that are applicable across various disciplines and real-life situations. Solving Worksheets plays a crucial role in developing essential mathematical skills, including problem-solving, critical thinking, logical reasoning, and numerical fluency.

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