Answer
$(-\infty, -\frac{3}{4})U(-\frac{3}{4},\infty)$
Work Step by Step
Step 1. As an absolute value returns a positive number or zero, the only case for the inequality not to be true is that $|4x+3|=0$
Step 2. Solve the above to get $x=-\frac{3}{4}$, exclude this point, we have the solution as $(-\infty, -\frac{3}{4})U(-\frac{3}{4},\infty)$
