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: Solve the inequality for \(x\)

Add \(9\) to all parts of \(0\leq3x - 9\leq12\).
\(0+9\leq3x-9 + 9\leq12 + 9\)
\(9\leq3x\leq21\)
Divide all parts by \(3\).
\(\frac{9}{3}\leq\frac{3x}{3}\leq\frac{21}{3}\)
\(3\leq x\leq7\)

Step2: Write in set - notation

Set - notation: \(\{x|3\leq x\leq7\}\)

Step3: Write in interval - notation

Interval - notation: \([3,7]\)

Answer:

Set notation: \(\{x|3\leq x\leq7\}\)
Interval notation: \([3,7]\)
For the graph, it should be a line segment on the number line starting at \(3\) (closed circle) and ending at \(7\) (closed circle). If we assume the options are based on standard number - line representations (where option C might be the one with closed circles at \(3\) and \(7\) and the line segment in between, but without seeing the exact scale of the options clearly from the given image description), the key is the interval \([3,7]\) which corresponds to a graph with endpoints included.