The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

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WORKSHEET 3.8: SOLVING ABSOLUTE VALUE EQUATIONS

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Follow the steps below to solve an absolute value equation:

1. Isolate the absolute value expression.


2. Write two equations.
   
   
   • One equation states that the expression in the absolute value symbols is positive.
   
   
   • The other equation states that the expression in the absolute value symbols is
     negative.
   
   
   
   


3. Solve each equation.


4. Check each solution in the original equation.

EXAMPLE

Solve forx.

| 2 x+ 4 |− 8 = 12

+ 8 + 8 Add 8 to isolate the absolute value expression.

| 2 x+ 4 |= 20 2 x+4 is written inside the absolute value symbols. It may equal 20 or

− 20. Write and solve two equations: 2 x+ 4 =20,x= 8 ,and 2 x+ 4 =− 20 ,

x=− 12.

DIRECTIONS: Solve each equation.

1. |x|= 8 2. |y− 3 |= 9


2. | 2 y− 1 |= 15 4. | 2 x+ 3 |= 11


3. |− 2 y+ 4 |= 10 6. | 2 x|− 4 = 2


4. |x− 3 |+ 2 = 8 8. | 5 −x|+ 9 = 12

CHALLENGE:April tried to solve| 3 x|− 3 =0 and concluded thatx=1. Her

answer was incorrect. What was her mistake? What is the correct answer?

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.