Question

match each compound inequality with its number line solution. show your work on a separate sheet of paper. 3w + 11 ≤ 13 or 3w ≥ 19 12 < k + 2 ≤ 18

Explanation:

Step1: Solve the first compound - inequality \(3w + 11\leq13\)

Subtract 11 from both sides: \(3w\leq13 - 11\), so \(3w\leq2\), then \(w\leq\frac{2}{3}\).

Step2: Solve the second part of the first compound - inequality \(3w\geq12\)

Divide both sides by 3: \(w\geq4\). The solution of \(3w + 11\leq13\) or \(3w\geq12\) is \(w\leq\frac{2}{3}\) or \(w\geq4\).

Step3: Solve the second compound - inequality \(12\lt k + 2\leq18\)

Subtract 2 from all parts: \(12-2\lt k+2 - 2\leq18 - 2\), so \(10\lt k\leq16\). This does not match any of the given number - line solutions shown.

The number - line with endpoints at \(\frac{2}{3}\) and 4 (closed circle at \(\frac{2}{3}\) and closed circle at 4) matches the solution of \(3w + 11\leq13\) or \(3w\geq12\).

Answer:

The number - line with endpoints at \(\frac{2}{3}\) and 4 (closed circles) matches the compound inequality \(3w + 11\leq13\) or \(3w\geq12\).