7th grade solving inequalities with negative coefficients worksheets
Eight inequalities using integers, fractions and decimals, with integer and half-integer boundaries. Undo the offset, then divide to isolate the variable.
Free printable PDF worksheet, aligned to Common Core 7.EE.B.4.b.
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The kind of problems you'll get
The variable represents a real number. Solve each inequality. Show your steps.
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−4/3 × m + 1/2 ≤ 11/6
Answer: m ≥ −1
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−4/3 × p − 7/2 > −29/6
Answer: p < 1
-
−3 × n − 3 < 6
Answer: n > −3
Every print pulls a fresh set of problems at this level, so a make-up test or a second sibling never gets the same sheet.
What's on a 7th grade sheet
- Solving inequalities with negative coefficients. The variable represents a real number. Solve each inequality. Show your steps. 8 problems per page.
Every version prints on US Letter or A4, with its answer key after the problems.
How to teach this
Test the boundary and a value in the solution set in the original inequality. Reverse the inequality when multiplying or dividing by a negative number.
Watch for: Adding or subtracting a negative number does not reverse the inequality. For < or >, leave out the boundary. For ≤ or ≥, include it.
Common questions about 7th grade solving inequalities with negative coefficients
- What does the answer key show?
- The complete key shows the solving steps, checks the boundary and tests one value in the solution set. Easy keys also test a value outside it. Choose Answers only for final answers without the worked steps.
- Does this sheet use fractions or decimals?
- Easy uses integers and integer boundaries. On-level adds fractions and decimals, with two half-integer boundaries. Difficult uses fractions and decimals, with six half-integer boundaries.
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- Solving inequalities with negative coefficients, all grades The full progression
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Aligned to Common Core 7.EE.B.4.b. Reviewed by the One more sheet team. Content version 241, updated October 2026.
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