Inequalities??? - College Level

<= means less than or equal to

If | x-2 | <= 9 , then a <= 2x - 1 <= b Find a and b.

Please explain how you got the answer!!! Thanks so much!!!

l x - 2 l ≤ 9
x - 2 ≤ 9
x ≤ 11

x - 2 ≥ -9
x ≥ -7

a ≤ 2x - 1 ≤ b
(a + 1)/2 ≤ x ≤ (b + 1)/2

(a + 1)/2 = -7 because x ≥ -7
2(a + 1)/2 = 2(-7)
a + 1 = -14
a = -15

Since x ≤ 11

(b + 1)/2 = 11
2(b + 1)/2 = 2(11)
b + 1 = 22
b = 21

a = -15
b = 21