Question

Eli attended a concert. The decibel level of the music averaged 110 decibels but varied by 28 decibels from the average. Enter and solve an absolute-value inequality to find the decibel range. Use d as your variable.

Answer 1

The decibel range is
`82\leq d\leq 138`

Explanation:

Let

d -----> the decibel level of the music

we know that

The absolute value of the difference of the decibel level of the music and its average, must be less than or equal to 28 decibels

so

The absolute value that represent this problem is

`\left|d-110\right|\le28`

Solve the absolute value

First solution (positive)

`+(d-110)\le28`

Adds 110 both sides

`d\le28+110`

`d\le138`

Second solution (negative)

`-(d-110)\le28`

Multiply by -1 both sides

`(d-110)\ge-28`

Adds 110 both sides

`d\ge-28+110`

`d\ge82`

therefore

The decibel range is

`82\leq d\leq 138`