Solving Linear Equations Online Practice

Question

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Question
Maluwa solves the inequality 3x+9≥6
. Which statement explains the steps she uses to find the solution set of the inequality?(1 point)
Responses

Maluwa subtracts 9 from both sides of the inequality and then multiplies both sides by 3 to obtain the solution x≥−9
.
Maluwa subtracts 9 from both sides of the inequality and then multiplies both sides by 3 to obtain the solution x greater-than-or-equal-to negative 9 .

Maluwa subtracts 9 from each side of the inequality and then divides both sides by 3 to obtain the solution x≥−1
.
Maluwa subtracts 9 from each side of the inequality and then divides both sides by 3 to obtain the solution x greater-than-or-equal-to negative 1 .

Maluwa adds 9 to each side of the inequality and then divides both sides by 3 to obtain the solution x≥5
.
Maluwa adds 9 to each side of the inequality and then divides both sides by 3 to obtain the solution x greater-than-or-equal-to 5 .

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
.

Answer 1

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

1. Subtract 9 from both sides: \[ 3x + 9 - 9 \geq 6 - 9 \quad \Rightarrow \quad 3x \geq -3 \]

2. Divide both sides by 3: \[ \frac{3x}{3} \geq \frac{-3}{3} \quad \Rightarrow \quad x \geq -1 \]

So, finally, the solution is \( x \geq -1 \).

The correct choices from the options you provided are:

• Maluwa subtracts 9 from each side of the inequality and then divides both sides by 3 to obtain the solution \( x \geq -1 \).
• Maluwa subtracts 9 from each side of the inequality and then divides both sides by 3 to obtain the solution \( x \) greater-than-or-equal-to negative 1.

Either of these statements accurately reflects the steps taken in solving the inequality.