How do you solve #abs(x - 7)<10#?

1 Answer
MeneerNask
Apr 1, 2015

Absolute value equations or inequalities must be split in two.

For #x>=7, (x-7)# is positive, so the inequality is

#x-7<10->x<17# (in total this means #7<=x<17#)

For #x<=7, (x-7)# is negative, but the absolute turns it around:

#7-x<10->x> -3# (this means #-3 < x <=7)#

Our total "solution space" is thus: #-3 < x<17#
graph{|x-7| [-16.38, 24.15, -4.57, 15.7]}

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