Question

which graph represents the solution set of the compound inequality $-4leq3x - 1$ and $2x + 4leq18$?

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 \(2x + 4\leq18\).
Subtract \(4\) from both sides: \(2x+4 - 4\leq18 - 4\), which simplifies to \(2x\leq14\).
Divide both sides by \(2\): \(\frac{2x}{2}\leq\frac{14}{2}\), so \(x\leq7\).

The solution of the compound - inequality \(-1\leq x\) and \(x\leq7\) is \(-1\leq x\leq7\).

Answer:

The graph with a closed - circle at \(-1\) and a closed - circle at \(7\) and the line segment between them.