Question

graph the set {x | -1 < x < 2} on the number line. then, write the set using interval notation. {x | -1 < x < 2} =

Explanation:

Step1: Understand the set notation

The set \(\{x \mid -1 < x < 2\}\) represents all real numbers \(x\) that are greater than \(-1\) and less than \(2\).

Step2: Determine interval notation

For an inequality \(a < x < b\) (where \(a\) and \(b\) are real numbers and \(a < b\)), the interval notation is \((a, b)\). Here, \(a=-1\) and \(b = 2\), so the interval notation is \((-1, 2)\).

(For graphing: We would place open circles at \(-1\) and \(2\) on the number line (since the inequality is strict, \(x\) cannot be equal to \(-1\) or \(2\)) and shade the region between them. But since the question also asks for interval notation, we focus on that part here.)

Answer:

\(\{x \mid - 1<x<2\}=(-1, 2)\)