Free Printable WorksheetMathAlgebra IMath CurriculumA-REI.3

ALG1.35 Compound Inequalities and Interval Solutions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.35 Compound Inequalities and Interval Solutions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.35 Compound Inequalities and Interval Solutions - Primary standard selected for prompt fields in this prompt cell: CCSS A-REI.3. Skill statement in this prompt cell: Select the correct solution to compound inequalities involving and and or; Select the representation that shows solution sets using interval notation and number lines. Associated standards listed with this skill in this prompt cell: CCSS: A-REI.3; A-CED.1,3; TEKS: §111.39(c)(2)(A–G) and (3)(B–E); VA SOL: A.EI.1 c; FL B.E.S.T.: MA.912.AR.2.6; NY-NGLS: AI-A.CED.1, AI-A.REI.1–3; CA CCSSM: A-REI.3; MA 2017: HS.A-REI.3; DoDEA CCRSM; NAEP: Algebra—inequalities; NCTM P2A: Practices 2, 5.. Use this prompt-provided wording as the supporting standard description for this workflow.

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 I

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 ALG1.35 Compound Inequalities and Interval Solutions skill assessments:

Problem 1Difficulty: Mastery
The solution set is -1 <= x < 4 or 8 <= x <= 10. Which interval notation represents it?
A[-1, 4) U [8, 10]
B(-1, 4] U (8, 10)
C[-1, 10]
D(-infinity, -1] U [4, 8) U (10, infinity)
Solution & Explanation:The first part is closed at -1 and open at 4. The second part is closed at both 8 and 10, and or joins the two intervals with a union.
Problem 2Difficulty: Mastery
A student solved -2x <= 8 as x <= -4. What is the best correction?
AThe solution should be x <= 4 because 8 divided by -2 is 4.
BThe solution should be x < -4 because <= always becomes <.
CThe student's solution is correct.
DThe solution should be x >= -4 because dividing by -2 reverses the inequality sign.
Solution & Explanation:When both sides are divided by a negative number, the inequality sign reverses. Since 8 divided by -2 is -4, the correct result is x >= -4.
Problem 3Difficulty: Mastery
Solve 2x + 5 >= 11 or 2x + 5 < 9. Which interval notation is correct?
A[2, 3)
B(-infinity, 2] U (3, infinity)
C(-infinity, 2) U [3, infinity)
D(-infinity, infinity)
Solution & Explanation:The first inequality gives x >= 3. The second gives x < 2. With or, the solution is (-infinity, 2) U [3, infinity).

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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 I Math students. It aligns with educational standard A-REI.3 (Primary standard selected for prompt fields in this prompt cell: CCSS A-REI.3. Skill statement in this prompt cell: Select the correct solution to compound inequalities involving and and or; Select the representation that shows solution sets using interval notation and number lines. Associated standards listed with this skill in this prompt cell: CCSS: A-REI.3; A-CED.1,3; TEKS: §111.39(c)(2)(A–G) and (3)(B–E); VA SOL: A.EI.1 c; FL B.E.S.T.: MA.912.AR.2.6; NY-NGLS: AI-A.CED.1, AI-A.REI.1–3; CA CCSSM: A-REI.3; MA 2017: HS.A-REI.3; DoDEA CCRSM; NAEP: Algebra—inequalities; NCTM P2A: Practices 2, 5.. Use this prompt-provided wording as the supporting standard description for this workflow.).

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