Answer: A. x <= -3
Explanation:
First, let's begin by simplifying the inequality:
-4x >= 12 ← To isolate the x, we need to divide both sides of the inequality by -4 (we must make this change to both sides so that the inequality is still valid). Remember that when dividing an inequality by a negative number, the orientation of the sign switches (greater than → less than, less than → greater then, etc.). So...
-4x / -4 <= 12 / -4 ← Simplify...
x <= -3
Now, we need to find the right number line representing this inequality.
- There should be a solid dot over -3, because the inequality includes the value -3 (x includes values less than and equal to -3).
- The number line should be pointing to the left, towards values less than -3.
The number line that fits these criteria would be A.