Question

Maluwa solves the inequality 3x + 9 >_ 6. Which statement explains the steps she uses to find the solution set of the inequality?
A. Maluwa adds 9 to each side of the inequality and then divides both sides by 3 to obtain the solution x >_ 5.
B. Maluwa subtracts 9 from each side of the inequality, divides both sides by 3, and reverses the inequality symbol to obtain the solution x <_ -1.
C. Maluwa subtracts 9 from both sides of the inequality and then multiplies both sides by 3 to obtain the solution x >_ -9.
D. Maluwa subtracts 9 from each side of the inequality and then divides both sides by 3 to obtain the solution x >_ -1.

Answer 1

To solve the inequality \(3x + 9 \geq 6\), Maluwa can follow these steps:

1. Subtract 9 from both sides:
\[
3x + 9 - 9 \geq 6 - 9
\]
This simplifies to:
\[
3x \geq -3
\]

2. Next, divide both sides by 3:
\[
\frac{3x}{3} \geq \frac{-3}{3}
\]
This simplifies to:
\[
x \geq -1
\]

Based on this process, Maluwa arrives at the solution \(x \geq -1\).

Thus, the correct statement for the explanation of the steps she uses is:

**D. Maluwa subtracts 9 from each side of the inequality and then divides both sides by 3 to obtain the solution x ≥ -1.**