# How do you solve abs(1-2x)>=13?

Apr 13, 2017

$x \le - 6 , x \ge 7$

#### Explanation:

$| 1 - 2 x | \ge 13$ needs to be broken into two problems:

$+ \left(1 - 2 x\right) \ge 13 \text{ and } - \left(1 - 2 x\right) \ge 13$

Solve each equation. Start with the positive equation:

$1 - 2 x \ge 13$

Subtract $1$ on both sides:
$- 2 x \ge 12$

Divide by $- 2$, be sure to flip the > to < because of the negative:
$x \le - 6$

Solve the negative equation:
$- \left(1 - 2 x\right) \ge 13$

Distribute the $- 1$:
$- 1 + 2 x \ge 13$

Add $1$ to both sides:
$2 x \ge 14$

Divide by $2$ on both sides:
#x >= 7

Answer: $x \le - 6 , x \ge 7$