Question

solve the inequality. express your answer using set notation and interval notation. graph the solution set.
0 ≤ 3x - 15 ≤ 6
the solution is expressed in set notation as {x|5 ≤ x ≤ 7}.
the solution is expressed in interval notation as 5,7.
choose the correct graph of the solution set below.

Explanation:

Step1: Add 15 to all parts of the inequality

$$0 + 15\leq3x-15 + 15\leq6 + 15$$
$$15\leq3x\leq21$$

Step2: Divide all parts by 3

$$\frac{15}{3}\leq\frac{3x}{3}\leq\frac{21}{3}$$
$$5\leq x\leq7$$

Answer:

Set - notation: \(\{x|5\leq x\leq7\}\)

Interval - notation: \([5,7]\)

For the graph, since the solution is \(5\leq x\leq7\), on the number - line, we have a closed - circle at \(x = 5\) and \(x=7\) (because the inequality includes equality) and a line segment connecting them. So the correct graph is the one that shows a segment between \(5\) and \(7\) with closed - circles at both endpoints.