Question

Find the solution set of the following inequalities and draw the graph of their solutions sets:
| x - 1 | > 3

Answer 1

We have
| x - 1 | > 3
Using prop. | x | ≥ a ⇔ ≥ a or x ≤ - a
Then | x - 1 | > 3 ⇔ x - 1 > 3 or x - 1 < (-3)
⇒ x > 4 or  x < - 2
so | x - 1 | > 3 {x : x < -2  or  x > 4}
The graph of this set is