Question

A safety regulation states that the height h of a guardrail should be 106 centimeters with an absolute deviation of no more than 7 centimeters. Write and solve an absolute value inequality that represents the acceptable heights of a guardrail.

Answer 1

The expected height is h = 106 cm.
The absolute deviation is 7 cm.

Therefore the range of acceptable heights, h, is
x  ≥ 106 - 7 or x ≥ 99 cm

Also,
x ≤ 106 + 7 = 113 cm

Therefore acceptable heights are defined by
99 ≤ x ≤ 113 cm

Answer:  99 ≤ h ≤ 113 cm