# What is the solution set for abs(x – 6) = 4?

Aug 10, 2015

With abosutes there are (usually) two solutions

#### Explanation:

(1)
$x \ge 6 \to x - 6 \ge 0$ the brackets don't have to do their work:
$\to x - 6 = 4 \to x = 10$
(2)
$x < 6 \to x - 6 < 0$ the brackets flip the sign:
$- \left(x - 6\right) = 4 \to - x + 6 = 4 \to x = 2$

Answer: $x = 2 \mathmr{and} x = 10$