Question

The temperature at noon in Los Angeles on a summer day was 88° F. During the day, the temperature varied from this by as much as 7.5° F. Write and solve an absolute-value inequality to find the range of possible temperatures for that day.

Answer 1

The range of possible temperatures is the interval [80.5°,95.5°]

Explanation:

Let

x -----> possible temperatures for that day.

we know that

The absolute value inequality of the difference of the possible temperatures and the temperature at noon must be less than or equal to 7.5° F

so

`\left|x-88\right|\le7.5`

Solve the absolute-value inequality

First case (positive case)

`+(x-88) \leq 7.5`

Adds 88 both sides

`x \leq 7.5+88`

`x \leq 95.5\°`

Second case (negative case)

`-(x-88) \leq 7.5`

Multiply by -1 both sides

`(x-88) \geq -7.5`

Adds 88 both sides

`x \geq -7.5+88`

`x \geq 80.5\°`

therefore

The range of possible temperatures is the interval [80.5°,95.5°]