When 24x-3 is non-negative, the following are true

1.   f(x) = |24x-3| = +(24x-3) = 24x-3

2.    24x-3 > 0
        24x > 3
          x > 
          x >  

Therefore f(x) = 24x-3 when x > 

When 24x-3 is negative, the following are true

1.   f(x) = |24x-3| = -(24x-3) = -24x+3

2.    24x-3 < 0
        24x < 3
          x < 
          x <  

Therefore f(x) = -24x+3 when x < 

Now we put those together:

f(x) =  24x-3 when x > 
f(x) = -24x+3 when x < 

We normally write this as:

       ì 24x-3 when x > 1/8
f(x) = í
       î-24x+3 when x < 1/8

The graph of f(x) looks like this:



Edwin