Question

graph the set {x | 1 ≤ x ≤ 7} on the number line. then, write the set using interval notation.

Explanation:

Step1: Identify the endpoints

The set is \(1\leq x\leq7\), so the endpoints are \(x = 1\) and \(x=7\).

Step2: Graph on number - line

On the number - line, place closed circles at \(x = 1\) and \(x = 7\) (since the inequalities are inclusive, \(\leq\)), and shade the region between them.

Step3: Write in interval notation

For a closed - interval from \(a\) to \(b\) (where \(a\leq x\leq b\)), the interval notation is \([a,b]\). Here \(a = 1\) and \(b = 7\), so the interval notation is \([1,7]\).

Answer:

Graph: Place closed circles at 1 and 7 and shade the region between them on the number - line. Interval notation: \([1,7]\)