# How do you solve abs(1/2x-1)<=3?

Mar 17, 2017

$- 4 \le x \le 8$

#### Explanation:

The solution to $| x | \le a$ is $- a \le x \le a$

We can apply this to the question here.

$- 3 \le \frac{1}{2} x - 1 \le 3$

To solve, isolate x in the central interval while leaving numeric values in the end intervals.

add 1 to ALL 3 intervals.

$- 3 + 1 \le \frac{1}{2} x \cancel{- 1} \cancel{+ 1} \le 3 + 1$

$\Rightarrow - 2 \le \frac{1}{2} x \le 4$

multiply ALL 3 intervals by 2

$\Rightarrow - 4 \le x \le 8 \text{ is the solution}$