Answer
$(-\infty, -\frac{7}{2})\cup(-\frac{1}{2}, \infty)$
Work Step by Step
Step 1. Rewrite the inequality as two cases:
(i) $2x+4\gt3$, and (ii) $2x+4\lt -3$
Step 2. For case (i), we have $x\gt -\frac{1}{2}$
Step 3. For case (ii), we have $x\lt -\frac{7}{2}$
Step 4. Thus, the solutions are
$(-\infty, -\frac{7}{2})\cup(-\frac{1}{2}, \infty)$
