Question

solve the compound inequality $-\frac{x}{2}<2$ and $3x + 1\leq25$. which of the options pictured shows the solutions on a number line?

Explanation:

Step1: Solve the first inequality

Solve \(-\frac{x}{2}<2\). Multiply both sides by \(- 2\). When multiplying an inequality by a negative number, the inequality sign flips. So \(x>-4\).

Step2: Solve the second inequality

Solve \(3x + 1\leq25\). Subtract \(1\) from both sides: \(3x\leq24\). Divide both sides by \(3\): \(x\leq8\).

Answer:

The solution of the compound inequality is \(-4 < x\leq8\). On a number - line, this is represented by an open circle at \(-4\) (because \(x>-4\), not \(x\geq - 4\)) and a closed circle at \(8\) (because \(x\leq8\)). So the answer is D.