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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 -2 -1 0 1 2. Ex: x = 5. What are the possible values of x?

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absolute value of x
Absolute Value (of x)
  • Symbol lxl
  • The distance x is from 0 on the number line.
  • Always positive
  • Ex: l-3l=3

-4 -3 -2 -1 0 1 2

ex x 5
Ex: x = 5
  • What are the possible values of x?

x = 5 or x = -5

to solve an absolute value equation
To solve an absolute value equation:

ax+b = c, where c>0

To solve, set up 2 new equations, then solve each equation.

ax+b = c or ax+b = -c

** make sure the absolute value is by itself before you split to solve.

ex solve 6x 3 15
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!

ex solve 2x 7 3 8
Ex: Solve 2x + 7 -3 = 8

Get the abs. value part by itself first!

2x+7 = 11

Now split into 2 parts.

2x+7 = 11 or 2x+7 = -11

2x = 4 or 2x = -18

x = 2 or x = -9

Check the solutions.

solving absolute value inequalities
Solving Absolute Value Inequalities
  • ax+b < c, where c>0

Becomes an “and” problem

Changes to: –c

  • ax+b > c, where c>0

Becomes an “or” problem

Changes to: ax+b>c or ax+b<-c

ex solve graph
Ex: Solve & graph.
  • Becomes an “and” problem

-3 7 8

solve graph
Solve & graph.
  • Get absolute value by itself first.
  • Becomes an “or” problem

-2 3 4

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