During a musical, an orchestra is playing. As the music plays, the volume changes at the beginning of the piece can be modeled b
y 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. Explain in words each step to find the following question: At what number(s) measures played would the sound level be at 80 decibels?
To find the range for the number of measures played to satisfy our solution, we must solve for x using s = 80. Next, we subtract 50 from both sides of the equation. Next, we divide both sides of the equation by 10 Next, to eliminate the absolute value bars, we will add a ± sign in front of our s value, 3. Finally, we add 4 to both sides of our equation giving us 4 ± 3 = x Separating this into two equations, we get 4 - 3 = x and 4 + 3 = x Therefore, x, the number of measures of music played, must be either 1 or 7.
