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

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Answer 1 · 2015-04-01T00:48:42

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]}

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