# Absolute Value Inequalities

In this video, we will be learning how to solve Absolute Value Inequalities. Remember to graph your inequalities!

When removing absolute value brackets, remember to flip the inequality sign and negate the other side of the inequality!

For Example:

$|2x-8|+8\geq14$

$|2x-8|+8-8\geq14-8\leftarrow$ Subtract 8 from both sides to isolate the quantities in the absolute value brackets

$|2x-8|\geq6\leftarrow$ Now remove the absolute value brackets and separate the equation into 2 cases as shown below

$2x-8\geq6$                                          $2x-8\leq-6$

$2x-8+8\geq6+8$                         $2x-8+8\leq-6+8$

$\frac{2x}{2}\geq\frac{14}{2}$                                                 $\frac{2x}{2}\leq\frac{2}{2}$

$x\geq7$                                                      $x\leq1$