# How do you solve and graph abs(x+5)<=9?

Jul 10, 2017

#### Answer:

With absolute values there are always two graphs, that meet at the point where the argument between the bars $= 0$

#### Explanation:

(1) $x \ge - 5$ no need for a sign change:
$x + 5 \le 9 \to x \le 9 - 5 \to x \le 4$

(2) $x < - 5 \to x + 5$ changes signs:
$- x - 5 \le 9 \to - x \le 9 + 5 \to - x \le 14 \to x \ge - 14$
graph{|x+5| [-20.63, 11.41, -4.28, 11.73]}