Question

which number line represents the solution set for the inequality 3x < -9?
four number line options:

1. left arrow, closed circle at -3, labeled -4, -3, -2, -1, 0, 1, 2, 3, 4
2. right arrow, closed circle at -3, labeled -4, -3, -2, -1, 0, 1, 2, 3, 4
3. left arrow, open circle at -3, labeled -4, -3, -2, -1, 0, 1, 2, 3, 4
4. right arrow, open circle at -3, labeled -4, -3, -2, -1, 0, 1, 2, 3, 4

Explanation:

Step1: Solve the inequality

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

Step2: Analyze the number line representation

For the inequality \( x < -3 \), we need an open circle at -3 (because -3 is not included in the solution set, since it's a strict inequality \( x < -3 \), not \( x \leq -3 \)) and the arrow pointing to the left (since we want all numbers less than -3).

Looking at the options:

• The first option has a closed circle at -3, which is for \( x \leq -3 \), so it's incorrect.
• The second option has a closed circle at -3 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 at -3 but arrow to the right, incorrect.

Answer:

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