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

1 Answer
Apr 2, 2015

In principle, an absolute equation can have two solutions.

(1)
If #x>=25->x-25>=0# so the equation is the same as:
#x-25=17->x=42#
(2)
If #x<25->x-25<0# but the absolute sign will turn this around:
#25-x=17->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)