Question

Find the solution set of the following inequalities and draw the graph of their solutions sets:
| 3 - 2x | ≥ 2

Answer 1

We have
| 3 - 2x | ≥ 2
Using prop. | x | ≥ a ⇔ x ≥ a or x ≤ - a
| 3 - 2x | ≥ 2
or 
3 - 2x ≤ -2 or (3 - 2x) ≥ 2
⇒ -2x ≤ -5 or -2x ≥ -1
⇒ 2x ≤ 1 or 2x ≥ 5
⇒ `x ≤ (1)/(2)  or  x ≥ (5)/(2)`
or
| 3 - 2x | ≥ 2 
⇒ `{x : x ≤ (1)/(2) or ≥ (5)/(2)}`
The graph of this set is