Question

graph the solution of $-4y \geq -12$ on a number line.
a
-10 -5 0 5 10
b
-10 -5 0 5 10
c
-10 -5 0 5 10
d
-10 -5 0 5 10

Explanation:

Step1: Solve the inequality

To solve \(-4y \geq -12\), we divide both sides by \(-4\). Remember that when we divide or multiply an inequality by a negative number, the direction of the inequality sign changes. So we have:

$$ \frac{-4y}{-4} \leq \frac{-12}{-4} $$

Simplifying both sides gives \(y \leq 3\).

Step2: Analyze the number line graphs

• For option A: The graph has a closed dot at 3 and the line is shaded to the left (towards negative numbers), which represents \(y \leq 3\).
• For option B: The closed dot is at -3, which does not match our solution.
• For option C: The closed dot is at 5, which does not match our solution.
• For option D: The closed dot is at -3 and the shading is to the right, which does not match our solution.

Answer:

A. The graph with a closed dot at 3 and shading to the left (from -10 to 3, with the arrow pointing left)