8th grade equations with infinitely many solutions worksheets
Six equations are true for every real value. Easier uses integer equations, including some with parentheses. On level adds expansion and signed fractions. 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.
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The kind of problems you'll get
The variable represents a real number. Show why each equation is true for every real value.
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2 × (3 × b + 5/4) = 6 × b + 5/2
Answer: 5/2 = 5/2 True for every real value. Infinitely many solutions.
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−2 × x + 4 = −2 × (x − 2)
Answer: 4 = 4 True for every real value. Infinitely many solutions.
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6 × x − 7/2 = 3 × (2 × x − 7/6)
Answer: −7/2 = −7/2 True for every real value. Infinitely many solutions.
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 infinitely many solutions. The variable represents a real number. Show why each equation is true for every real value. 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 and cancel equal variable terms. A true constant statement such as 3 = 3 shows that the original equation holds for every real value. Testing a few values alone does not establish this; explain why each algebraic step preserves the equation.
Watch for: When variable terms cancel, read the remaining statement before drawing a conclusion. Checking one value cannot prove that every real value is a solution.
Common questions about 8th grade equations with infinitely many solutions
- 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 true statement. It explains why all real numbers are solutions. Choose Answers only for final answers without the worked steps.
- What numbers are used?
- Easier uses integer coefficients and constants. On level adds fractions and expansion. Harder includes mixed fractions and decimals, hundredths and more sign changes. Every equation has all real numbers as its solution set.
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 infinitely many solutions, 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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