During a musical an orchestra is playing. As the music plays, the volume changes in the beginning of the piece can be modeled by the equation s = 10│x - 4│+ 50 where s represents the sound level in decibels and x represents the number of measures of music played. At what number(s) measures played would the sound level be at 80 decibels?

The sound level would be at 80 decibels at 1 or 7 number of measures played

Step-by-step explanation:

Equations with Absolute Values

We have the function s to represent the sound level in decibels:

Where x is the number of measures of the music played.

We are required to find the value of x that makes s=80 decibels. We have to find the equation:

Subtracting 50:

Dividing by 10:

For the absolute value be equal to 3, its argument could be positive or negative:

Or

This leads us to two solutions:

x=7

Or

x=1

The sound level would be at 80 decibels at 1 or 7 number of measures played

step-by-step explanation: