Question

graph the set {x | 5 < x < 7} on the number line. then, write the set using interval notation.

Explanation:

Step1: Locate endpoints on number - line

On the number - line, mark open circles at \(x = 5\) and \(x = 7\) since the inequalities are strict (\(<\)). Then shade the region between these two open - circles.

Step2: Write in interval notation

For an open interval from \(a\) to \(b\) (where \(a\lt x\lt b\)), the interval notation is \((a,b)\). Here \(a = 5\) and \(b = 7\), so the interval notation is \((5,7)\).

Answer:

On the number - line, mark open circles at 5 and 7 and shade the region between them. The interval notation is \((5,7)\)