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

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WORKSHEET 3.9: SOLVING ABSOLUTE VALUE EQUATIONS

THAT HAVE TWO SOLUTIONS, ONE SOLUTION, OR NO SOLUTION

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Follow the guidelines below to solve absolute value equations:

1. Isolate the absolute value expression.


2. If the absolute value equation equals
   
   
   • A positive number, there are two solutions
   
   
   • A negative number, the equation has no solution
   
   
   • Zero, there is one solution
   
   
   
   

EXAMPLES

Positive number Negative number Zero

|x+ 1 |= 10 | 2 x|=− 2 |x− 3 |= 0

Write two equations. No solution. Write one equation.

x+ 1 = 10 x+ 1 =− 10 x− 3 = 0

x=9andx=− 11 x= 3

DIRECTIONS: Solve each equation, if possible, or state if the equation has no solution.

1. |x− 3 |= 15 2. |x+ 5 |= 0 3. |y− 2 |=− 3


2. |y|− 3 =− 3 5. − 2 |x+ 1 |=− 10 6. | 2 y+ 3 |= 7


3. − 3 +|x− 5 |=− 1 8. 2 |x+ 7 |=− 1 9. 2 |x− 1 |= 4


4. |x− 5 |+ 12 = 10 11. − 3 |x+ 7 |= 30 12. − 4 |x+ 8 |+ 13 =− 11

CHALLENGE:Write an absolute value equation that has one solution,x=2.

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Copyright

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