Question

what is the solution set for $-6x - 8 \geq 16$?
a $x \geq \frac{4}{3}$
b $x \leq -\frac{4}{3}$
c $x \leq -4$
d $x \geq 4$

Explanation:

Step1: Add 8 to both sides

We start with the inequality \(-6x - 8 \geq 16\). First, we add 8 to both sides to isolate the term with \(x\). So, \(-6x - 8 + 8 \geq 16 + 8\), which simplifies to \(-6x \geq 24\).

Step2: Divide by -6 (reverse inequality)

Next, we divide both sides by -6. When we divide or multiply an inequality by a negative number, we must reverse the inequality sign. So, \(\frac{-6x}{-6} \leq \frac{24}{-6}\), which simplifies to \(x \leq -4\).

Answer:

C. \(x \leq -4\)