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.

Question

Mathematics

Khan

19 April, 01:10

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.

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Answers (1)

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Gregory Compton · 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