Question

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

Answer 1

`99\leq h\geq 113`

Explanation:

Given:

Height of the guardrail = 106 cm

Deviation in height = 7 cm.

We need to write the inequality that represents the acceptable height of a guardrail.

Solution:

From the given statement the height of the guardrail is 106 cm with 7 cm deviation.

So, we write the absolute value inequality as:

`|h-106|\leq 7`

Now, we solve the inequality.

`-7\leq h-106\geq 7`

Add 106 in whole equation.

`-7+106\leq h-106+106\geq 7+106`

`99\leq h\geq 113`

Therefore, the height of the guardrail must be 99 cm to 113 cm.