Free Printable WorksheetMathGrade 6Math Curriculum6.EE.B.8

6.72 Write Inequalities to Model Constraints and Graph Them Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 6 Math worksheet provides structured practice on 6.72 Write Inequalities to Model Constraints and Graph Them. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Which inequality and number-line graph correctly represent the constraint in the problem? (CCSS 6.EE.B.8; CA 6.EE.B.8; MA 6.EE.B.8; NY NY-6.EE.8; TX 19 TAC §111.26(b)(9)(A)-(B); FL MA.6.AR.1.2; VA 6.PFA.4a-e)

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 6

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 6.72 Write Inequalities to Model Constraints and Graph Them skill assessments:

Problem 1Difficulty: Mastery

A digital timer counts a response as quick only when the time is under 10.01 seconds. Let t represent the response time in seconds. Which choice matches the constraint and its number-line graph?

At <= 10.01; closed circle at 10.01, shade left

Bt > 10.01; open circle at 10.01, shade right

Ct < 10.01; open circle at 10.01, shade left

Dt < 10.01; open circle at 10.01, shade right

Solution & Explanation:In this problem, under 10.01 seconds means t < 10.01. The boundary value 10.01 is not included, so the graph uses a open circle at 10.01 and shades left for values that are less than 10.01.

Problem 2Difficulty: Mastery

A measuring cup is acceptable if the error is at most 0.6 milliliter. Let E represent the measurement error in milliliters. Which model shows both the inequality and the correct graph?

AE <= 0.6; closed circle at 0.6, shade left

BE < 0.6; open circle at 0.6, shade left

CE >= 0.6; closed circle at 0.6, shade right

DE <= 0.6; closed circle at 0.6, shade right

Solution & Explanation:In this problem, at most 0.6 milliliter means E <= 0.6. The boundary value 0.6 is included, so the graph uses a closed circle at 0.6 and shades left for values that are less than or equal to 0.6.

Problem 3Difficulty: Mastery

A bike race time trial advances riders with speeds greater than 16.2 miles per hour. Let v represent the speed in miles per hour. Which option gives the correct inequality and matching number-line graph?

Av >= 16.2; closed circle at 16.2, shade right

Bv < 16.2; open circle at 16.2, shade left

Cv > 16.2; open circle at 16.2, shade left

Dv > 16.2; open circle at 16.2, shade right

Solution & Explanation:In this problem, greater than 16.2 miles per hour means v > 16.2. The boundary value 16.2 is not included, so the graph uses a open circle at 16.2 and shades right for values that are greater than 16.2.

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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 6 Math students. It aligns with educational standard 6.EE.B.8 (Write Inequalities to Model Constraints and Graph Them).