# How do you solve abs(2x-9)<=11?

Apr 17, 2018

$x \le 10 \mathmr{and} x \ge - 1$

#### Explanation:

$| 2 x - 9 | \le 11$

We need to start by solving the absolute value

We know either $2 x - 9 \le 11 \mathmr{and} 2 x - 9 \ge - 11$

Now we can solve the first one:

$2 x - 9 \le 11$

Add $9$ on both sides

$2 x - 9 + 9 \le 11 + 9$

$2 x \le 20$

Divide both sides by $2$

$\frac{\cancel{2} x}{\cancel{2}} \le \frac{20}{2}$

$x \le 10$

Now we can solve the second one

$2 x - 9 \ge - 11$

Add $9$ on both sides

$2 x - 9 + 9 \ge - 11 + 9$

$2 x \ge - 2$

Then divide both sides by $2$

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

$x \ge - 1$

Thus,

$x \le 10 \mathmr{and} x \ge - 1$