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

8.66 Checking and Validating Solutions to Linear Equations Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.66 Checking and Validating Solutions to Linear Equations. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.66 Checking and Validating Solutions to Linear Equations - Which substitution check correctly verifies whether the proposed value is a solution? (CCSS 8.EE.C.7; CA 8.EE.C.7; MA 8.EE.C.7)

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 8.66 Checking and Validating Solutions to Linear Equations skill assessments:

Problem 1Difficulty: Hard

Diego checked y = 5 in 4(y + 1) = 24 and wrote, "4(5) + 1 = 24" Which statement best describes the mistake?

AThe student compared the two sides correctly but made a final conclusion error.

BThe student dropped the term inside the parentheses and checked 4(5) + 1 instead of keeping the entire expression inside the parentheses.

CThe student replaced the variable on both sides, but the arithmetic after substitution is the only problem.

DThe student should have solved the equation instead of checking it by substitution.

Solution & Explanation:The work "4(5) + 1 = 24" is not a correct substitution check for 4(y + 1) = 24. The student dropped the term inside the parentheses and checked 4(5) + 1 instead of keeping the entire expression inside the parentheses.

Problem 2Difficulty: Hard

Which student's check of x = 18 for x/5 - 3 = 1 is correct?

AXavier says, "(18)/8 = 1. This becomes 2.25 = 1, so x = 18 is not a solution."

BVictor says, "(18)/5 - 3 = 1. This becomes 0.6 = 1, so x = 18 is not a solution."

CWren says, "5/(18) - 3 = 1. This becomes -49/18 = 1, so x = 18 is not a solution."

DYara says, "(18)/5 + 3 = 1. This becomes 6.6 = 1, so x = 18 is not a solution."

Solution & Explanation:Victor is correct. Substituting 18 into x/5 - 3 = 1 gives (18)/5 - 3 = 1, and that simplifies to 0.6 = 1.

Problem 3Difficulty: Hard

Ben tried to verify j = 4 for 2(j + 3) + 1 = j + 11 by writing, "2(4) + 3 + 1 = (4) + 11" Which explanation is correct?

AThe student only made a small arithmetic slip after a correct substitution.

BThe student compared both sides correctly, but the final conclusion sentence is missing.

CThe student should have combined like terms before replacing the variable.

DThe student dropped part of the grouped expression instead of substituting into the entire quantity inside the parentheses.

Solution & Explanation:The work "2(4) + 3 + 1 = (4) + 11" is not a correct substitution check for 2(j + 3) + 1 = j + 11. The student dropped part of the grouped expression instead of substituting into the entire quantity inside the parentheses.

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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.7 (Primary standard selected for prompt fields: CCSS 8.EE.C.7. Skill statement: Which substitution check correctly verifies whether the proposed value is a solution? Associated standards listed with this skill: CCSS 8.EE.C.7; CA 8.EE.C.7; MA 8.EE.C.7. Use this embedded wording as the best available supporting standard description for this workflow.).