Functions and Transformations

Lesson 8

Math

Unit 5

9th Grade

Lesson 8 of 16

Objective


Solve absolute value equations algebraically and identify extraneous solutions.

Common Core Standards


Core Standards

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

Foundational Standards

  • 8.EE.C.7
  • 8.EE.C.8

Criteria for Success


  1. Solve absolute value equations algebraically, including those with variables on both sides of the equation. 
  2. Understand that solutions can sometimes give rise to extraneous solutions.
  3. Identify extraneous solutions by checking solutions algebraically or graphically.

Tips for Teachers


This lesson addresses a specific standard in the Massachusetts state frameworks: A-REI.3a, "Solve linear equations and inequalities in one variable involving absolute value."

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Anchor Problems


Problem 1

Solve each absolute value equation algebraically.

a.   $${18=3|x-1|}$$

b.  $${|4x|+9=17}$$

c.  $${-|3x+1|=-13}$$

Guiding Questions

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Problem 2

Use the absolute value equation below to answer the questions that follow.

$${|x+4|=2x}$$

  1. Solve the equation algebraically.
  2. Graph the equation as a system of two equal functions. 
  3. Do your algebraic solutions match your graphical solutions? Does this equation have any extraneous solutions? Explain.

Guiding Questions

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Problem 3

Solve the absolute value equation algebraically. Check for extraneous solutions. 

$${|3x+3|=x+5}$$

Guiding Questions

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Problem Set


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

Target Task


Solve the absolute value equation algebraically. Check for extraneous solutions.

$${|2x+3|=3x+1}$$

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.

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Lesson 7

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Lesson 9

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Piecewise Functions

Topic B: Absolute Value Functions

Topic C: Function Transformations

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