The following equation represents the value (y) of a car based on its age (x).
[tex]y=-800x+12000[/tex]
We are told that the value of a car of the given model, based on its age, is less than $6000.
So, we can write
[tex]6000<-800x+12000[/tex]
Let us solve the above inequality for x.
[tex]\begin{gathered} 6000<-800x+12000 \\ 6000-12000<-800x \\ -6000<-800x \\ \frac{-6000}{-800}<\frac{-800x}{-800} \\ 7.5>x \\ x<7.5 \end{gathered}[/tex]
This means that the age of the car is less than 7.5 years.
Therefore, the possible range of values that could represent the age of the car is 0 to 7.5 years.
[tex]0
