Question

Given the function `f(x)= 0.5abs(x -4)-3`, for what values x is f(x)=7?

Answer 1

`x = 24` and `x = -16`

Explanation:

Given `f(x) = 0.5abs(x - 4) - 3` and `f(x) = 7` we can write:

`0.5abs(x - 4) - 3 = 7`

Now, we must isolate the absolute value term while keeping the equation balanced:

`0.5abs(x - 4) - 3 + 3 = 7 + 3`

`0.5abs(x - 4) - 0 = 10`

`0.5abs(x - 4) = 10`

`(0.5abs(x - 4))/0.5 = 10/0.5`

`(cancel(0.5)abs(x - 4))/cancel(0.5) = 20`

`abs(x - 4) = 20`

Because the absolute value function converts any number to a positive number we must solve the term within the absolute value for both 20 and -20:

`x - 4 = 20`

`x - 4 + 4 = 20 + 4`

`x - 0 = 24`

`x = 24`

and

`x - 4 = -20`

`x - 4 + 4 = -20 + 4`

`x - 0 = -16`

`x = -16`