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.

The absolute value inequality is_ .

The acceptable range of heights of a guardrail are _cm to _cm.

Answer 1

Answer: We are given:

The height h of a guardrail = 106 centimeters

Absolute deviation = 7 centimeters

The absolute value inequality is
`|x-106|\leq 7`

To find the acceptable heights of a guardrail , we add and subtract absolute deviation(7) from the mean height(106)

The acceptable range of height is:

106 + 7 = 113

106 - 7 = 99

Acceptable heights are defined by

`99 cm \leq h\leq 113cm`

Therefore, the acceptable range of heights of a guardrail are 99 cm to 113 cm.