5x − 7 > 18
Show answer
x > 5
Free printable worksheet
Solving Inequalities Worksheet
Twenty inequalities covering inverse operations, sign reversal, compound inequalities, and absolute value.
Algebra 1Grades 7-103 pagesAnswer key included
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What this worksheet includes
- Twenty inequalities covering inverse operations, sign reversal, compound inequalities, and absolute value.
- 3-page printable PDF with a complete answer key
- Designed for Grades 7-10 algebra 1 practice
- Available as an immediate free download with no email required
How to use it
Use this solving 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 7-10 students working on algebra 1. 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 Algebra I worksheets.
Topic guide
How to approach solving inequalities
Solving an inequality uses the same balancing process as solving an equation, with one essential exception: multiplying or dividing by a negative number reverses the inequality symbol.
Students progress from single inequalities to compound and absolute-value forms. Each answer should be written with the correct symbol and, when requested, represented on a number line with an open or closed endpoint.
Learning objectives
- Isolate a variable in one-step and multi-step inequalities
- Reverse the inequality after multiplying or dividing by a negative
- Interpret compound inequalities and number-line endpoints
Skills to review first
- Solving linear equations
- Comparing signed numbers
- Reading interval direction on a number line
Worked example
Follow the reasoning step by step
Solve −3(2x − 1) ≤ 15.
- Distribute: −6x + 3 ≤ 15.
- Subtract 3: −6x ≤ 12.
- Divide by −6 and reverse ≤ to ≥.
- Write the solution: x ≥ −2.
Solution: x ≥ −2, shown with a closed point at −2 and shading to the right.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
−2y + 4 ≤ 10
Show answer
y ≥ −3
3 ≤ 2x + 1 < 11
Show answer
1 ≤ x < 5
Error check
Common mistakes to watch for
- Reversing the symbol after adding a negative instead of dividing by one
- Forgetting to reverse the symbol after division by a negative
- Using a closed endpoint for < or >