Question

which number line represents the solution set for the inequality 3x < -9? (four number line options are shown, with different markings at -3 and different arrow directions)

Explanation:

Step1: Solve the inequality

To solve \( 3x < -9 \), divide both sides by 3. Since 3 is positive, the inequality sign remains the same. So we have \( x < \frac{-9}{3} = -3 \).

Step2: Analyze the number line representation

• The solution \( x < -3 \) means we need an open circle at -3 (because -3 is not included in the solution set, since the inequality is strict, \( < \), not \( \leq \)) and the arrow pointing to the left (towards numbers less than -3).

Looking at the options:

• The first option has a closed circle, which is for \( \leq \) or \( \geq \), so it's incorrect.
• The second option has a closed circle and arrow to the right, incorrect.
• The third option has an open circle at -3 and arrow to the left, which matches \( x < -3 \).
• The fourth option has an open circle but arrow to the right, incorrect.

Answer:

The third number line (with open circle at -3 and arrow pointing left)