Question

which graph represents the solution set of the compound inequality -4 ≤ 3x - 1 and 2x + 4 ≤ 10?

Explanation:

Step1: Solve the first inequality

Solve $- 4\leq3x - 1$. Add 1 to both sides: $-4 + 1\leq3x-1 + 1$, which simplifies to $-3\leq3x$. Divide both sides by 3: $\frac{-3}{3}\leq\frac{3x}{3}$, so $- 1\leq x$.

Step2: Solve the second inequality

Solve $2x + 4\leq10$. Subtract 4 from both sides: $2x+4 - 4\leq10 - 4$, which simplifies to $2x\leq6$. Divide both sides by 2: $\frac{2x}{2}\leq\frac{6}{2}$, so $x\leq3$.

Step3: Determine the solution set

The solution of the compound - inequality is $-1\leq x\leq3$. On a number line, this is represented by a line segment from - 1 to 3, with closed circles at - 1 and 3.

Answer:

The graph that has a closed - circle at $x=-1$, a closed - circle at $x = 3$, and a line segment connecting them.