8th grade solving equations with variables on both sides worksheets
These eight equations have variable terms on both sides and one solution each. Easier uses integer coefficients and two fractional solutions. On level starts with four integer equations, followed by four with fractions. Harder includes close fractional coefficients, more negative coefficients after collection, and five noninteger solutions. The default key shows the solving steps and checks both sides of the original equation.
Free printable PDF worksheet, aligned to Common Core 8.EE.C.7.b.
Each print is a different sheet with its own answer key. You don't need to sign up.
Need one more? These are the skills next door at this grade.
The kind of problems you'll get
Solve for the unknown variable. Show your steps and check your answer in the original equation.
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3 × x − 6 = x + 2
Answer: x = 4
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3 × x − 6 = 4 × x − 2
Answer: x = −4
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3 × y − 1 = −y − 5
Answer: y = −1
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 variables on both sides. Solve for the unknown variable. Show your steps and check your answer in the original equation. 8 problems per page.
Every version prints on US Letter or A4, with its answer key after the problems.
How to teach this
Ask which variable term your child will remove first and why. Keep both sides balanced at each step, then substitute the answer to check it.
Watch for: Apply the same operation to both sides of the equation. Keep the sign when subtracting a variable term or dividing by a negative coefficient.
Common questions about 8th grade solving equations with variables on both sides
- What does the answer key show?
- By default, each solution includes the equation steps, reasons and a check in both original sides. Choose Answers only for final answers without the worked steps.
- What numbers are used?
- Easier and on level have six integer solutions and two half-integer solutions. Harder has three integer and five noninteger solutions. Each setting includes exactly one zero solution, and solution magnitudes stay at or below 4.
- Can an equation have no solution?
- Every equation on this sheet has exactly one solution. Classifying other solution sets is a separate lesson.
Related worksheets
- 8th grade classifying linear solution sets Same grade, nearby skill
- 8th grade clearing fractional coefficients Same grade, nearby skill
- 8th grade equations in mixed numeric representations Same grade, nearby skill
- 8th grade equations requiring collection of like terms Same grade, nearby skill
- Solving equations with variables on both sides, all grades The full progression
- All 8th grade math worksheets Every skill at this level
- All 8th grade worksheets Everything at this level
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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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