Free Printable WorksheetMathAlgebra IIMath CurriculumA-REI.12

ALG2.128 Rational Inequalities Worksheet

Q: How do I download and print this ALG2.128 Rational Inequalities worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

Q: Is this ALG2.128 Rational Inequalities worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

Q: Can students practice ALG2.128 Rational Inequalities online with instant feedback?

Yes! In addition to this printable worksheet, students can practice ALG2.128 Rational Inequalities interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

Q: What 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.12 (Primary standard selected for prompt fields in this prompt cell: CCSS A-REI.12. Skill statement in this prompt cell: Select the correct solution(s) to rational inequalities using sign charts and critical points, and graph solution sets with excluded values. Associated standards listed with this skill in this prompt cell: CCSS A-REI.12; CA CCSSM A-REI.12; MA 2017 A-REI.12; NY NGLS A-REI.12; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.).

Download our free printable Algebra II Math worksheet on ALG2.128 Rational Inequalities. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

Choose your preferred download format:

100% Free • No registration or login required • Instant file access

Download PDF

Prefer interactive practice with instant grading and explanations?Practice Rational Inequalities Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.128 Rational Inequalities. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.128 Rational Inequalities - Primary standard selected for prompt fields in this prompt cell: CCSS A-REI.12. Skill statement in this prompt cell: Select the correct solution(s) to rational inequalities using sign charts and critical points, and graph solution sets with excluded values. Associated standards listed with this skill in this prompt cell: CCSS A-REI.12; CA CCSSM A-REI.12; MA 2017 A-REI.12; NY NGLS A-REI.12; TX TEKS Algebra II: §111.40. 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 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 ALG2.128 Rational Inequalities skill assessments:

Problem 1Difficulty: Mastery

First move all terms to one side, then solve the rational inequality (3x³ + 19x² - 66x - 88)/((x + 8)x(x - 5)) < 2. Which solution set is correct?

A(-11, -8) U (-4, 0) U (2, 5)

B(-infinity, -11] U [-8, -4]

C(-infinity, -11)

D(-infinity, -11] U [-11, -8] U [-8, -4] U [-4, 0] U [0, 2] U [2, 5] U [5, infinity)

Solution & Explanation:Subtract 2 from both sides to get ((x + 11)(x + 4)(x - 2))/((x + 8)x(x - 5)) < 0. Critical points are -11, -8, -4, 0, 2, and 5; denominator zeros (-8, 0, and 5) are excluded. Testing intervals gives (-11, -8) U (-4, 0) U (2, 5).

Problem 2Difficulty: Mastery

First move all terms to one side, then solve the rational inequality (-x³ + 8x² + 28x - 141)/((x + 1)(x - 6)) >= 1. Which solution set is correct?

A(-infinity, -5] U [-1, 3]

B(-infinity, -5] U (-1, 3] U (6, 9]

C(-infinity, -5) U (-5, -1) U (-1, 3) U (3, 6) U (6, 9) U (9, infinity)

D(-infinity, -5) U (-5, -1)

Solution & Explanation:Subtract 1 from both sides to get (-(x + 5)(x - 3)(x - 9))/((x + 1)(x - 6)) >= 0. Critical points are -5, -1, 3, 6, and 9; denominator zeros (-1 and 6) are excluded. Testing intervals gives (-infinity, -5] U (-1, 3] U (6, 9].

Problem 3Difficulty: Mastery

Solve the original rational inequality ((x + 6)(x - 1)(x - 8))/((x + 6)(x + 2)(x - 4)) <= 0. Remember that any denominator zero is excluded even if a factor cancels. Which solution set is correct?

A(-infinity, -6) U (-6, -2) U (1, 4) U (8, infinity)

B(-2, 1) U (4, 8)

C(-2, 1] U (4, 8]

D[-6, -2] U [1, 4]

Solution & Explanation:Simplify only after noting the restrictions. Critical points are -6, -2, 1, 4, and 8, and denominator zeros (-6, -2, and 4) cannot be included even if a factor cancels. The sign chart gives (-2, 1] U (4, 8].

Want more practice questions with step-by-step guidance?

Practice All Questions Online

Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this ALG2.128 Rational Inequalities worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this ALG2.128 Rational Inequalities worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice ALG2.128 Rational Inequalities online with instant feedback?

Yes! In addition to this printable worksheet, students can practice ALG2.128 Rational Inequalities interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

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.12 (Primary standard selected for prompt fields in this prompt cell: CCSS A-REI.12. Skill statement in this prompt cell: Select the correct solution(s) to rational inequalities using sign charts and critical points, and graph solution sets with excluded values. Associated standards listed with this skill in this prompt cell: CCSS A-REI.12; CA CCSSM A-REI.12; MA 2017 A-REI.12; NY NGLS A-REI.12; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.).