Question

solve the inequality. express your answer using set notation and interval notation. graph the solution set.
0 < 3x - 9 < 12
the solution is expressed in set notation as {x|}
the solution is expressed in interval notation as
choose the correct graph of the solution set below.

Explanation:

Step1: Add 9 to all parts

$$\begin{align*} 0+9&\leq3x - 9+9\leq12 + 9\\ 9&\leq3x\leq21 \end{align*}$$

Step2: Divide all parts by 3

$$\begin{align*} \frac{9}{3}&\leq\frac{3x}{3}\leq\frac{21}{3}\\ 3&\leq x\leq7 \end{align*}$$

Answer:

• Set - notation: $\{x|3\leq x\leq7\}$
• Interval - notation: $[3,7]$
• Graph: Option B (assuming the graph in option B has a closed - circle at \(x = 3\) and \(x=7\) and the line segment between them on the number line)