Solving Absolute Value Equations

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Solving Absolute Value Equations Inequalities
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Absolute Value (of x)

• Symbol lxl
• The distance x is from 0 on the number line.
• Always positive
• Ex l-3l3

-4 -3 -2 -1 0 1
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Ex x 5

• What are the possible values of x?
• x 5 or x -5

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To solve an absolute value equation

• axb c, where cgt0
• To solve, set up 2 new equations, then solve each
  equation.
• axb c or axb -c
• make sure the absolute value is by itself
  before you split to solve.

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Ex Solve 6x-3 15

• 6x-3 15 or 6x-3 -15
• 6x 18 or 6x -12
• x 3 or x -2
• Plug in answers to check your solutions!

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Ex Solve 2x 7 -3 8

• Get the abs. value part by itself first!
• 2x7 11
• Now split into 2 parts.
• 2x7 11 or 2x7 -11
• 2x 4 or 2x -18
• x 2 or x -9
• Check the solutions.

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Solving Absolute Value Inequalities

• axb lt c, where cgt0
• Becomes an and problem
• Changes to cltaxbltc
• axb gt c, where cgt0
• Becomes an or problem
• Changes to axbgtc or axblt-c

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Ex Solve graph.

• Becomes an and problem

-3 7 8
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Solve graph.

• Get absolute value by itself first.
• Becomes an or problem

-2 3 4