Lesson 11 | Solving One-Variable Equations | 8th Grade Mathematics

Objective

Solve and graph inequalities with variables on one side of the inequality (optional).

Common Core Standards

Core Standards

The core standards covered in this lesson

A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Reasoning with Equations and Inequalities

A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Foundational Standards

The foundational standards covered in this lesson

7.EE.B.4.B

Expressions and Equations

7.EE.B.4.B — Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Solve inequalities with variables on one side and use substitution to check answers.
Accurately multiply and divide with negative coefficients in inequalities, paying close attention to the direction of the inequality symbol.
Graph solutions to inequalities.
Write, solve, and interpret solutions to inequalities for applications.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lessons 11 and 12 extend on 7.EE.4b and bridge a gap to high school standard A.REI.3. Inequalities are not included in the 8th grade standards, but this is a natural extension of students’ work with equations from earlier in the unit, especially now that students are able to work with more complex equations and inequalities. These two lessons can be treated as optional.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

25-30 minutes

Problem 1

Solve the inequality. Then pick a value for $$x$$ and check your answer. Lastly, graph your solution on a number line.

$$8-4(x-2)+6(x-1)>20$$

Guiding Questions

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Student Response

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Problem 2

Solve the inequality.

$${4-{x\over3}\leq {3\over4}(32)}$$

Guiding Questions

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Student Response

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Problem 3

Noah is creating a rectangular picture frame out of wood. He wants the width of the frame to be 6 inches more than half the length. If Noah has a total of 60 inches of wood that he can use for the frame, write and solve an inequality to represent the possible measurements of the length of the frame.

Guiding Questions

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Student Response

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

5-10 minutes

Solve each inequality, then represent the solutions on a number line.

a. $${{{-2x+4}\over5} \geq 18}$$

b. $${{3\over5}(10-15x)+13x > -20}$$

Student Response

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Include problems similar to Anchor Problems #1 and #2.

Kuta Software Free Pre-Algebra Worksheets Inequalities — Multi-Step Inequalities (Use only those inequalities with variables on one side; the others can be used for Lesson 12.)
Kuta Software Free Algebra 1 Worksheets Inequalities — Multi-Step Inequalities (Use only those inequalities with variables on one side; the others can be used for Lesson 12.)
Illustrative Mathematics Sports Equipment Set
Algebra By Example 5.1 Adding and Subtracting Inequalities
Algebra By Example 5.2 Multiplying and Dividing Inequalities

Solving One-Variable Equations

Objective

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Common Core Standards

Core Standards

Reasoning with Equations and Inequalities

Foundational Standards

Expressions and Equations

Criteria for Success

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Tips for Teachers

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Anchor Problems

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Problem 1

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Guiding Questions

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Problem 2

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Guiding Questions

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Problem 3

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Guiding Questions

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Problem Set

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Target Task

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Additional Practice

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