Question

A safety regulation states that the height hh 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

Let us say that h is the height of the guardrail. Therefore the inequality equation that we can generate from this scenario is:

| h – 106 | = ± 7

There are two ways to solve this, either the equation is positive or negative.

When the equation is positive, therefore:

| h – 106 | = 7

h = 7 + 106 = 113 cm

When the equation is negative, therefore:

| h – 106 | = - 7

h = -7 + 106 = 99 cm

So the height must be 99 cm to 113 cm