3x + 2 ≤ 14
Show answer
x ≤ 4
Free printable worksheet
Inequalities Worksheet
Twenty one-step, two-step, and multi-step inequalities including sign reversal.
Middle School MathGrades 6-83 pagesAnswer key included
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What this worksheet includes
- Twenty one-step, two-step, and multi-step inequalities including sign reversal.
- 3-page printable PDF with a complete answer key
- Designed for Grades 6-8 middle school math practice
- Available as an immediate free download with no email required
How to use it
Use this inequalities worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 6-8 students working on middle school math. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Middle School Math worksheets.
Topic guide
How to approach inequalities
An inequality describes a range of values rather than one value. Solve it like an equation, but reverse the inequality symbol whenever multiplying or dividing both sides by a negative number.
Graph solutions with an open endpoint for < or > and a closed endpoint for ≤ or ≥. Shade toward all values that make the original statement true.
Learning objectives
- Solve one- and multi-step inequalities
- Reverse symbols correctly
- Graph solutions on a number line
Skills to review first
- Linear equations
- Comparing signed numbers
- Number-line direction
Worked example
Follow the reasoning step by step
Solve −4x + 3 > 19.
- Subtract 3: −4x > 16.
- Divide both sides by −4.
- Reverse > to < because the divisor is negative.
- Graph an open point at −4 and shade left.
Solution: x < −4.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
−2y ≥ 10
Show answer
y ≤ −5
5 − x < 8
Show answer
x > −3
Error check
Common mistakes to watch for
- Reversing after adding a negative
- Forgetting to reverse after negative division
- Using the wrong endpoint type