Solving Inequalities Worksheets

Free Solving Inequalities Worksheets with Answer Keys

Looking for a solving inequalities worksheet or two to give your students some extra practice with working with and solving inequalities>

If so, on this page you will find a free library of PDF Solving Inequalities Worksheets. Each printable worksheet includes a variety of practice problems for topics including solving and graphing inequalities on a number line, solving one-step inequalities, solving two-step inequalities, and solving multi-step inequalities.

Each solving inequalities worksheet can be downloaded as a printable PDF file that includes a complete answer key. You can preview and/or download any worksheet by clicking on any of the blue text links shared in the library below. When you click on a link, you can preview the worksheet and the corresponding answer key along with the option to save the file or send it to your printer to be printed in either black-and-white or in color.

Directly below the solving inequalities worksheet library, you will find a review section that includes a few step-by-step example problems of how to solve inequalities in case you or your students need a quick tutorial on how to solve the types of problems that you will find on our solving inequality worksheets.

All of the free PDF worksheets included in the library below are sample worksheets from the Mashup Math K-12 Infinite Math Worksheet Libraries , where you can download hundreds of printable topic-specific math worksheets. Quick Reference: How to Download/Print Our Worksheets

Solving Inequalities Worksheets

▶️ Graphing single-variable inequalities on a number line (A)

▶️ Graphing single-variable inequalities on a number line (B)

▶️ Solving one-step inequalities (A)

▶️ Solving one-step inequalities (B)

▶️ Solving two-step inequalities (A)

▶️ Solving two-step inequalities (B)

▶️ Solving multi-step inequalities (A)

▶️ Solving multi-step inequalities (B)

🛑 WAIT! Do You Want More Free Math Worksheets?

Be sure to visit the Mashup Math Practice Worksheets Library, where you will find hundreds of free PDF math worksheets with complete answer keys for Grades K-12, Algebra, and Geometry!

Solving Inequalities Worksheet Review

In case you need some help with any of the problems on the solving inequality worksheets share above, this section will serve as a quick review of some important vocabulary words and concepts related to solving inequalities.

For starters, it is important to understand that there are four types of inequalities:

• > : greater than

• < : less than

• ≥ : greater than or equal to

• ≤ : less than or equal to

So, for example, the inequality x > 7 means that x is greater than 7 (but not equal to 7). On the other hand, the inequality x ≤ -3 means that x is less than or equal to -3 (meaning that -3 is a possible solution for x).

The corresponding number line graphs to these two example inequalities, x > 7 and x ≤ -3, are shown in Figure 01 below. Notice how the graph of the first example, x > 7, includes an open circle (since 7 is not included), while the second graph of x ≤ -3 includes a closed circle (since -3 is included in the solution set).

Now let’s take a look at a practice problem similar to one you would see on a solving inequalities worksheet in the library above.

Let’s consider the inequality 3x + 8 < 26.

To solve this inequality, we can think of the < symbol like an equals sign (=) and solve for x using inverse operations like we would an algebraic expression. Our goal here is to get the variable, x, by itself, and we can do that as follows:

• 3x + 8 < 26

• 3x +8 -8 < 26 -8

• 3x < 18

• (3x)/3 < 18/3

• x < 6

By performing inverse operations, we were able to isolate the variable, x, and conclude that the solution to the inequality is x < 6.

The mathematical steps to solving this problem are shown in Figure 02 below.

Now let’s take a look at one more example where we have to solve the inequality (x/3) - 6 > 2.

Just like the previous example, we can use some basic algebra skills to isolate the variable, x, and solve the inequality as follows:

• (x/3) - 6 > 2

• (x/3) -6 +6 > 2 + 6

• (x/3) > 8

• (x/3)(3) > 8(3)

• x > 24

Now we have x by itself and the inequality has been solved. We can now conclude that the solution to the inequality (x/3) - 6 > 2 is x > 24.

Figure 03 below shows the step-by-step process to solving this second example.

Do you need more help with learning how to solve inequalities?

If so, check out our free How to Solve Inequalities Tutorial, which includes several step-by-step examples and practice problems.