If |2x - 4| ≤ 10, then which of the following intervals represents all possible values of 3x + 5?

Question: If |2x - 4| ≤ 10, then which of the following intervals represents all possible values of 3x + 5?

Solution:
The given inequality:
|2x - 4| ≤ 10
⇒ - 10 ≤ 2x - 4 ≤ 10
⇒ - 10 + 4 ≤ 2x - 4 + 4 ≤ 10 + 4
⇒ - 6 ≤ 2x ≤ 14
⇒ - 3 ≤ x ≤ 7
Multiply the interval by 3:
3(- 3) ≤ 3x ≤ 3(7)
⇒ - 9 ≤ 3x ≤ 21

Add 5 to the interval:
⇒ - 9 + 5 ≤ 3x + 5 ≤ 21 + 5
∴ - 4 ≤ 3x + 5 ≤ 26