Question

solve the compound inequality.
5 < 3x + 5 ≤ 20
graph the solution on the number line.

Explanation:

Step1: Subtract 5 from all parts

Subtract 5 from \(5<3x + 5\leq20\).
\[5-5<3x+5 - 5\leq20 - 5\]
\[0<3x\leq15\]

Step2: Divide all parts by 3

Divide \(0<3x\leq15\) by 3.
\[\frac{0}{3}<\frac{3x}{3}\leq\frac{15}{3}\]
\[0 < x\leq5\]

Answer:

The solution of the compound - inequality is \(0 < x\leq5\). On the number - line, we use an open circle at \(x = 0\) (because \(x>0\)) and a closed circle at \(x = 5\) (because \(x\leq5\)) and draw a line segment connecting them.