Question

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

Answer 1

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]}