# How do you solve and write the following in interval notation: | 3 − 2x | − 8 ≥ 1?

May 29, 2016

$x \le - 3$ or $x \ge 6$

#### Explanation:

$| 3 - 2 x | - 8 \ge 1$ means $| 3 - 2 x | \ge 9$

Now $| a | \ge b$ means either $a \ge b$ or $- a \ge b$

Hence, $| 3 - 2 x | \ge 9$ means

either $3 - 2 x \ge 9$ i.e. $- 2 x \ge 9 - 3$ or $- 2 x \ge 6$ i.e. $x \le - 3$

or $- \left(3 - 2 x\right) \ge 9$ i.e. $- 3 + 2 x \ge 9$ or $2 x \ge 12$ i.e. $x \ge 6$