What numbers are used?

Easier has eight integer solutions. On level has six integer and two half-integer solutions. Harder has three integer and five noninteger solutions. Each setting includes exactly one zero solution.

What does the key show?

By default, each key shows two separate expansions, the solving steps with reasons, and the exact solution. Choose Answers only for final answers without the worked steps.

8th grade solving equations with expansion on both sides

8th grade solving equations with expansion on both sides worksheets

These eight equations have a grouped expression on each side and one exact solution. Easier uses integer values and mostly positive outside factors. On level includes all four positive and negative factor pairings, with integer and fractional factors. Harder combines more negative and improper fractional factors with five noninteger solutions. Students expand both groups and solve.

Free printable PDF worksheet, aligned to Common Core 8.EE.C.7.b.

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The kind of problems you'll get

Solve for the unknown variable. Show your steps.

2 × (n − 3/2) = −3 × (−4/3 × n − 1)
Answer: n = −3
2 × (2 × x − 2) = 3 × (1/3 × x − 1/3)
Answer: x = 1
−2 × (2 × x − 3/2) = 3 × (−1/3 × x + 1)
Answer: x = 0

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 an 8th grade sheet

Solving equations with expansion on both sides. Solve for the unknown variable. 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

Write each expansion separately so both products can be checked. Once the parentheses are removed, apply the same operation to both sides.

Watch for: Multiply every term inside each group by its outside factor. Keep the negative sign when distributing a negative factor.

Common questions about 8th grade solving equations with expansion on both sides

What numbers are used?: Easier has eight integer solutions. On level has six integer and two half-integer solutions. Harder has three integer and five noninteger solutions. Each setting includes exactly one zero solution.
What does the key show?: By default, each key shows two separate expansions, the solving steps with reasons, and the exact solution. Choose Answers only for final answers without the worked steps.

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Aligned to Common Core 8.EE.C.7.b. Reviewed by the One more sheet team. Content version 241, updated October 2026.

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