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Solving Absolute Value Equations

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Solving Absolute Value Equations & Inequalities Absolute Value (of x) Symbol lxl The distance x is from 0 on the number line. Always positive Ex: l-3l=3 -4 -3 ... – PowerPoint PPT presentation

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Title: Solving Absolute Value Equations


1
Solving Absolute Value Equations Inequalities
2
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
2
3
Ex x 5
  • What are the possible values of x?
  • x 5 or x -5

4
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.

5
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!

6
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.

7
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

8
Ex Solve graph.
  • Becomes an and problem

-3 7 8
9
Solve graph.
  • Get absolute value by itself first.
  • Becomes an or problem

-2 3 4
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