Absolute value Equation and Inequalities

Absolute Value- Distance from zero

                          |-3|=3

When working with absolute Value, your answer should always be positive, if you are trying to figure out |-9| the anwer is always going to be the same number without the negative sign.

ex.|x|+5=11

          -5   -5

          |x|=6

           x=6,-6

When solving absolute value equations, set up two new equations. One positive and one negitive. Then solve each equation, and those are both your answers.

ex. |x=5|=9

   x=5=9        x+5=-9

         -5              -5   -5

    x=4            x=-14

ex. True or false?

|3x-6|=-2

False, the answer can never be a negitive.

|x-8|=2

true, x can be 10 or -10.

ex. solve the equations and graph answer.

|3x+5|=12

 3x+5=-12          3x+5=12

        -5                      -5

  3x=-17                3x=7

   /3     /3                 /3   /3

  x=-5.66                  x= 2.33

                 x=5.66 or 2.33.