Question

How do you solve `|5x + 2| - 2< 3`?

Answer 1

You may always add or subtract from both sides:

Explanation:

`|5x-2|<5`

As long as `x>=2/5` the inequality stays as is:
`5x-2<5`
`->5x<7->x<7/5`

When `x<2/5` the signs between the bars are flipped:
`-5x+2<5`
`->-5x<3->5x> -3->x> -3/5`

Both combined: `-3/5 < x <7/5`

The solutions are in the triangle between the graph of `|5x-2|-5=0` and the `x`-axis:
graph{|5x-2|-5 [-6.473, 7.574, -6.39, 0.633]}