Question

1. which graph correctly shows the solution of the compound inequality ( 3xgeq - 12 ) and ( 8xleq 16 )?

Explanation:

Step1: Solve the first inequality

Solve \(3x\geq - 12\). Divide both sides by 3: \(x\geq\frac{-12}{3}\), so \(x\geq - 4\).

Step2: Solve the second inequality

Solve \(8x\leq16\). Divide both sides by 8: \(x\leq\frac{16}{8}\), so \(x\leq2\).

The solution of the compound inequality \(3x\geq - 12\) and \(8x\leq16\) is \(-4\leq x\leq2\). On a number - line, this is represented with a closed circle at \(x = - 4\) (because \(x=-4\) is included in the solution, due to \(x\geq - 4\)) and a closed circle at \(x = 2\) (because \(x = 2\) is included in the solution, due to \(x\leq2\)) and a line segment connecting them.

Answer:

The third graph (the one with a red - filled circle at \(-4\) and a red - filled circle at \(2\) and a red line segment between them) is the correct graph.