#### Answer

($x\leq -4$) U ($x\geq 3$)

#### Work Step by Step

$$|2x + 1| \geq 7$$ This inequality can be broken down into the following system of inequalities: ($2x + 1 \geq 7$) or ($2x + 1 \leq -7$) We can now continue by solving each individually: $$2x + 1 \geq 7$$ $2x \geq 7 - 1$ $\frac{2x}{2} \geq \frac{6}{2}$ $x \geq 3$ $$2x + 1 \leq -7$$ $2x \leq -7 - 1$ $\frac{2x}{2} \leq \frac{-8}{2}$ $x \leq -4$ By combining each solution, we can express the answer of the exercise as follows: ($x\leq -4$) U ($x\geq 3$)