# How do you graph and solve  abs[2-x/2]-1<=1?

May 16, 2018

$0 \le x \le 8$ or $x \in \left[0 , 8\right]$

#### Explanation:

Add one to both sides to get:
$\left\mid 2 - \frac{x}{2} \right\mid \le 1$

Now since we have $\left\mid \right\mid$ we ca take the positive or negative of the function:

$2 - \frac{x}{2} \le 2$
$- \frac{x}{2} \le 0$
$- x \le 0$
$x \ge 0$

or

$\frac{x}{2} - 2 \le 2$
$\frac{x}{2} \le 4$
$x \le 8$

Combining these gives us:
$0 \le x \le 8$ or $x \in \left[0 , 8\right]$