8th grade equations with no solution worksheets
Six equations lead to a false constant statement. Easier uses matching variable terms on both sides with integer coefficients. On level adds expansion. Harder has three collection tasks and three tasks mixing fractions and decimals, with more opposing signs and decimals such as 0.05 and -0.15.
Free printable PDF worksheet, aligned to Common Core 8.EE.C.7.a.
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
The variable represents a real number. Show why each equation has no solution.
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2 × (2 × w + 1) = 4 × w − 2
Answer: 2 = −2 False statement. No solution.
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2 × m − 2 = 2 × (m − 1/2)
Answer: −2 = −1 False statement. No solution.
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3 × e + 4 = 3 × e − 4
Answer: 4 = −4 False statement. No solution.
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
- Equations with no solution. The variable represents a real number. Show why each equation has no solution. 6 problems per page.
Every version prints on US Letter or A4, with its answer key after the problems.
How to teach this
Collect each side before cancelling equal variable terms. Ask why a false statement such as 3 = 4 rules out every real value. Keep each sign when collecting terms on either side.
Watch for: When variable terms cancel, read the remaining statement before drawing a conclusion. One value that fails is not enough to prove that an equation has no solution.
Common questions about 8th grade equations with no solution
- What does the answer key show?
- By default, the key shows any needed expansion, conversion and collection, cancellation of the variable terms and the final false statement. It explains why no real value solves the equation. Choose Answers only for final answers without the worked steps.
- What numbers are used?
- Easier uses integer coefficients and constants. On level adds expansion. Harder includes mixed fractions and decimals, hundredths and more sign changes. Variables range over the real numbers.
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
- Equations with no solution, 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.a. Reviewed by the One more sheet team. Content version 241, updated October 2026.
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