Chapter 1 - Expressions, Equations, and Inequalities - 1-5 Solving Inequalities - Lesson Check - Page 37: 3

$x\leq-2$

First, we distribute. We have $-4(3x+2)\geq16$ is $-12x-8\geq16$. Now we add both sides by 8 to get $-12x-8+8\geq16+8$, which is $-12x\geq24$. Now, we divide both sides by $-12$. Also, because we are dividing across the inequality by a negative number, we need to flip the sign from $\geq$ to $\leq$. We have $\frac{-12x}{-12}\leq\frac{24}{-12}$ which is $x\leq-2$.