Free Printable WorksheetMathGrade 8Math Curriculum8.EE.C.7a

8.68 Creating Equations with One, No, or Infinite Solutions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.68 Creating Equations with One, No, or Infinite Solutions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.68 Creating Equations with One, No, or Infinite Solutions - Which equation would have exactly one solution, no solution, or infinitely many solutions as requested? (CCSS 8.EE.C.7a; CA 8.EE.C.7a; MA 8.EE.C.7a)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 8

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 8.68 Creating Equations with One, No, or Infinite Solutions skill assessments:

Problem 1Difficulty: Hard
Which equation with variable s has no value that makes it true?
A6(s + 2) - 6 = 3(s + 5) + 6
B0.5(12s - 12) + 2 = -5
C2(s - 2) + 6 = 2(s + 2) + 2
D2(s - 4) + (s + 3) = 3s - 5
Solution & Explanation:Simplify 2(s - 2) + 6 = 2(s + 2) + 2 to get 2s + 2 = 2s + 6. The s-terms match, but the constants are different, so no value of s makes the equation true.
Problem 2Difficulty: Hard
Which equation is true for every value of j?
A0.5(8j + 10) - 4 = 4j - 4
B(1/3)(6j - 9) = -3j - 16
C0.5(4j + 4) + 3 = -6j - 8
D-2j + 6 + j = -3j + 6 + 2j
Solution & Explanation:Distribute and combine like terms in -2j + 6 + j = -3j + 6 + 2j. You get -j + 6 = -j + 6, so the equation is an identity with infinitely many solutions.
Problem 3Difficulty: Hard
Which equation has infinitely many solutions? Focus on what happens after you combine like terms.
A0.5(4h + 4) + 6 = 2h + 8
B0.5(12h - 8) - 2 = 2h - 15
C5(h + 5) + (h + 5) = -14
D3(h - 4) - 2(h - 1) = h + 18
Solution & Explanation:0.5(4h + 4) + 6 = 2h + 8 simplifies to 2h + 8 = 2h + 8. Because both sides are equivalent, the equation is true for all values of h.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.EE.C.7a (Primary standard selected for prompt fields: CCSS 8.EE.C.7a. Skill statement: Which equation would have exactly one solution, no solution, or infinitely many solutions as requested? Associated standards listed with this skill: CCSS 8.EE.C.7a; CA 8.EE.C.7a; MA 8.EE.C.7a. Use this embedded wording as the best available supporting standard description for this workflow.).

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