Question

How do you solve `absx - 1 < 4`?

Answer 1

Given `abs(x) - 1 <4`

Since you can always add any amount to both sides of an inequality without effecting the orientation of the inequality, this is equivalent to
`abs(x) <5`

This means that either
Case 1: `x>=0` and `x <5`

or
Case 2: `x<0` and `x> -5`

Combining Case 1 and Case2, we have the solution set
`-5 < x < +5`