I think you meant (24x+4)^(-1)<0.
This is equivalent to 1 / [4(6x+1)] < 0.
We must determine the set of values of x for which 6x+1 is not equal to zero and 6x+1 is less than 0 (because 1 / [4(6x+1)] < 0 for such values).
Solve 6x+1 < 0. 6x+1<0 becomes 6x < -1, or x < -1/6
This divides the number line into two halves: (- infinity, -1/6) and (-1/6, infinity).
From each half, choose an x value not equal to -1/6. If the original inequality is then true, you have found the interval that solves it. If false, choose the other interval to represent your solution.
