Question

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

Explanation:

Step1: Solve the inequality

Divide both sides of \(3x < - 9\) by \(3\).
$$x<\frac{-9}{3}$$
$$x < - 3$$

Step2: Analyze the number - line representation

When \(x < - 3\), on the number line, there is an open circle at \(-3\) (because \(-3\) is not included in the solution set) and the arrow points to the left (towards smaller numbers).

Answer:

The third number - line (with an open circle at \(-3\) and arrow pointing to the left) represents the solution set of the inequality \(3x < - 9\).