# How do you solve abs(x - 25)= 17?

Apr 2, 2015

In principle, an absolute equation can have two solutions.

(1)
If $x \ge 25 \to x - 25 \ge 0$ so the equation is the same as:
$x - 25 = 17 \to x = 42$
(2)
If $x < 25 \to x - 25 < 0$ but the absolute sign will turn this around:
$25 - x = 17 \to x = 8$
graph{|x-25| [-28.57, 103.1, -21.2, 44.67]}
Estimate the $y = 17$ horizontal line, and you see what I mean
(you can zoom in or out in the graph)