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