Question

write the set {x | x < - 3} using interval notation, then graph the set on a number line. (-3,∞) (-∞,-3) choose the correct graph below.

Explanation:

Step1: Recall interval - notation rules

For \(x < a\), the interval notation is \((-\infty,a)\). Here \(a=-3\), so the interval notation for \(x < - 3\) is \((-\infty,-3)\).

Step2: Recall number - line graphing rules

When graphing \(x < - 3\) on a number line, we use an open - circle at \(-3\) (because \(x\) is strictly less than \(-3\)) and draw an arrow to the left (towards negative infinity).

Answer:

Interval notation: \((-\infty,-3)\)
Graph: Option B (an open - circle at \(-3\) and an arrow pointing to the left)