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

8.91 Interpreting and Checking Reasonableness of Algebraic 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 8.91 Interpreting and Checking Reasonableness of Algebraic Solutions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.91 Interpreting and Checking Reasonableness of Algebraic Solutions - Which choice is the most reasonable solution in context, and which check supports it? (CCSS 8.EE.C.7; CCSS 8.F.B.4; CA 8.EE.C.7; MA 8.EE.C.7)

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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 8.91 Interpreting and Checking Reasonableness of Algebraic Solutions skill assessments:

Problem 1Difficulty: Hard

Solve 1.5n + 4 = 4n + 4 for n, which represents the integer location on a number line. Which option best checks and interprets the result?

An = 0, and 1.5(0) + 4 and 4(0) + 4 both equal 4, but it is not reasonable. It is not reasonable because the value should be positive.

Bn = 1, but 1.5(1) + 4 = 5.5 and 4(1) + 4 = 8, so this value does not solve the equation.

Cn = 0, and 1.5(0) + 4 and 4(0) + 4 both equal 4, so the solution is reasonable. The value stays a whole number, and negative values are allowed if needed.

Dn = -1, but 1.5(-1) + 4 = 2.5 and 4(-1) + 4 = 0, so this value does not solve the equation.

Solution & Explanation:Move the variable terms to one side and the constants to the other to get -2.5n = 0, then divide by -2.5. This gives n = 0. Checking shows that 1.5(0) + 4 and 4(0) + 4 both equal 4. 0 is reasonable, and this quantity is tracked in whole-number steps.

Problem 2Difficulty: Hard

Solve 0.5(e - 4) = 5e - 2 for e, which represents the number of entry passes printed for a museum trip. Which option best checks and interprets the result?

Ae = 0, and 0.5(0 - 4) and 5(0) - 2 both equal -2, but it is not reasonable. It is not reasonable because the value should be greater than 0.

Be = 1, but 0.5(1 - 4) = -1.5 and 5(1) - 2 = 3, so this value does not solve the equation.

Ce = -1, but 0.5(-1 - 4) = -2.5 and 5(-1) - 2 = -7, and the value is not reasonable anyway. A count cannot be negative.

De = 0, and 0.5(0 - 4) and 5(0) - 2 both equal -2, so the solution is reasonable. This count is a whole number and not negative.

Solution & Explanation:Expand the parentheses to get 0.5e - 2 = 5e - 2. Then combine like terms to get -4.5e = 0 and divide by -4.5. This gives e = 0. Checking shows that 0.5(0 - 4) and 5(0) - 2 both equal -2. 0 is reasonable because this count can be zero.

Problem 3Difficulty: Hard

Nina checked the equation 0.5b = b + 2.5 and concluded that b = -4. If b stands for the basement level in a building, which statement is true?

ANina is correct because 0.5(-4) = -2 and -4 + 2.5 = -1.5.

BNina is not correct because there is no reasonable solution in this context.

CNina is not correct. The equation solves to b = -5, and 0.5(-5) and -5 + 2.5 both equal -2.5. The value stays a whole number, and negative values are allowed if needed.

DThe better answer is b = -6 because 0.5(-6) = -3 and -6 + 2.5 = -3.5.

Solution & Explanation:Expand the parentheses to get 0.5b = b + 2.5. Then combine like terms to get -0.5b = 2.5 and divide by -0.5. This gives b = -5. Checking shows that 0.5(-5) and -5 + 2.5 both equal -2.5. This quantity can be negative, but it must stay a whole number, so the value makes sense.

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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 choice is the most reasonable solution in context, and which check supports it? Associated standards listed with this skill: CCSS 8.EE.C.7; CCSS 8.F.B.4; CA 8.EE.C.7; MA 8.EE.C.7. Use this embedded wording as the best available supporting standard description for this workflow.).