You are building a rock wall for a flower bed along your 46-foot long driveway. You want the wall to be one-half of the length of the driveway with an absolute deviation of at most 6 feet. Write and solve an absolute value inequality that represents the possible lengths of the wall.

a. ║ x - 23 ║ ≤ 6 b.  17 ≤ x ≤ 29

Step-by-step explanation:

a. Let x be the length of the wall. Since the length of the wall is half the length of the drive way with an absolute deviation of 6 at most, since the drive way is 46 foot long, half of it is 46/2 = 23.

So, 23 ± 6 ≤ x or x - 23 ≤ ±6 or ║ x - 23 ║ ≤ 6

b. Solving the absolute value inequality,

-(x - 23) ≤ 6 and x - 23 ≤ 6

x - 23 ≥ 6 and x - 23 ≤ 6

x ≥ 23 - 6 and x ≤ 23 + 6

x ≥ 17 and x ≤ 29

So 17 ≤ x ≤ 29