Please solve: |x - 8| < 5?

|x - 8| < 5

An inequality in the form |z| < c translates to the compound inequality:
-c < z < c

Applying the same concept, we get

-5 < x - 8 < 5

And now, we isolate x by adding 8 to each part of the compound inequality.

3 < x < 13

|x - 8| < 5
x - 8 < 5 , x - 8 > -5

x - 8 < 5
x < 5 + 8
x < 13

x - 8 > -5
x > -5 + 8
x > 3

∴ 3 < x < 13

Inequality problem

x - 8 is greater than -5 and smaller than +5

-5 < x - 8 < 5

then we get
3 < x 13

- 5 < x - 8 < 5

- 3 < x < 13