Question

which number line represents the solution set for the inequality $3x < - 9$?

Explanation:

Step1: Solve the inequality

Given \(3x < - 9\), divide both sides by \(3\).
\(x <\frac{-9}{3}\)

Step2: Simplify the right - hand side

\(\frac{-9}{3}=-3\), so \(x < - 3\)

On a number line, for \(x < - 3\), there is an open circle at \(-3\) (because the inequality is strict, \(x\) cannot equal \(-3\)) and the line extends to the left (towards more negative numbers)

Answer:

The third option (the number line with an open circle at \(-3\) and the line extending to the left)