Free Printable WorksheetMathAlgebra IIMath CurriculumA-REI.2

ALG2.18 Checking Domains and Constraints After Solving Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.18 Checking Domains and Constraints After Solving. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.18 Checking Domains and Constraints After Solving - Recheck solutions against original constraints (denominators, radicals, logarithm arguments, context limits) and remove invalid solutions. Associated source-listed standards: CCSS A-REI.2; F-IF.2; CA CCSSM A-REI.2; F-IF.2; MA 2017 A-REI.2; F-IF.2; NY NGLS A-REI.2; F-IF.2; TX TEKS Algebra II: §111.40.

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

Algebra II

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 ALG2.18 Checking Domains and Constraints After Solving skill assessments:

Problem 1Difficulty: Mastery
For (x + 5)/(x2 - 25) = 1/(x - 5), a student concludes all real numbers except x = 5 solve the equation. What is missing from the check?
ANothing is missing
Bx = -5 must also be excluded because it makes the original denominator 0
Cx = 0 must be excluded
DThe equation has no solution
Solution & Explanation:The left side has denominator x2 - 25, so both x = 5 and x = -5 are excluded from the original domain.
Problem 2Difficulty: Mastery
If an equation simplifies to an identity after canceling a factor, then every real number is a solution, even any value that makes the canceled factor 0.
ATrue
BFalse
Solution & Explanation:Canceled-factor values are still excluded because they were never in the original domain. An identity only holds for the values that keep the original expression defined.
Problem 3Difficulty: Mastery
Solving sqrt(x + 10) = x + 4 gives candidates x = -1 and x = -6. Which explanation is correct?
ABoth stay because both solve the squared equation
BOnly x = -6 stays because it is smaller
COnly x = -1 stays because x + 4 must be nonnegative in the original equation
DNeither stays because radicals never have negative solutions
Solution & Explanation:In the original equation, the right side is x + 4, so it must be nonnegative. x = -1 works, but x = -6 makes the right side negative and fails the check.

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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 Algebra II Math students. It aligns with educational standard A-REI.2 (Recheck solutions against original constraints (denominators, radicals, logarithm arguments, context limits) and remove invalid solutions. Associated source-listed standards: CCSS A-REI.2; F-IF.2; CA CCSSM A-REI.2; F-IF.2; MA 2017 A-REI.2; F-IF.2; NY NGLS A-REI.2; F-IF.2; TX TEKS Algebra II: §111.40.).

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