Question

which number line shows the solution to the inequality? -3x + 6 ≤ 15

Explanation:

Step1: Subtract 6 from both sides

To isolate the term with \( x \), we subtract 6 from both sides of the inequality \(-3x + 6 \leq 15\).
\[
-3x + 6 - 6 \leq 15 - 6
\]
\[
-3x \leq 9
\]

Step2: Divide by -3 (reverse inequality)

When dividing an inequality by a negative number, we reverse the inequality sign. Divide both sides by -3:
\[
\frac{-3x}{-3} \geq \frac{9}{-3}
\]
\[
x \geq -3
\]

Step3: Identify the number line

The solution \( x \geq -3 \) means we have a closed dot at -3 (since the inequality is "greater than or equal to") and the line extends to the right. Looking at the number lines, the first number line (top - most) has a closed dot at -3 and extends to the right, which matches our solution.

Answer:

The first number line (with closed dot at -3 and extending to the right)