Question

Let f(x) = x + |2x − 1|. find all solutions to the equation f(x) = 8. (enter your answers as a comma-separated list. if an answer does not exist, enter dne.)

Answer 1

Hi !

f(x) = x + |2x − 1|

We have the function at hand,so if the function is equal to 8,then x + |2x − 1| is equal to 8 too :

x + |2x − 1| = 8

Now we can express the module so:

|2x − 1| = 8-x

It means we'll have 2 options :

I : 2x-1 = 8-x

II : 2x-2 = -(8-x)

I : 2x-1 = 8-x | +x

2x-1+x = 8-x+x

3x-1 = 8 | + 1

3x-1+1 = 8+1

3x = 9 | ÷ 3

x = 3

II : 2x-1 = -(8-x)

2x-1 = -8+x | -x

2x-x-1 = -8+x-x

x-1 = -8 | +1

x-1+1 = -8+1

x = -7

Solutions : 3,-7