Question

Find the solution set of the following inequalities and draw the graph of their solutions sets:
`| x + 5 | < 8`

Answer 1

We have
`| x + 5 | < 8`
Using prop. | x | < a ⇔ - a < x < a
⇒ -8 < x + 5 < 8
⇒ -5 -8 < x < 8 - 5
⇒ -13 < x < 3
The graph of this set is