Which answer gives all the values of x for which the inequality

Question

3x + 2 >/ 9 - 4x is true?
A. x > 1
B. x <_ 1
C. x >_ 1
D. x = 1

Answer 1

To solve the inequality \( 3x + 2 \geq 9 - 4x \), we can first isolate \( x \). Here are the steps:

1. Add \( 4x \) to both sides: \[ 3x + 4x + 2 \geq 9 \] This simplifies to: \[ 7x + 2 \geq 9 \]

2. Subtract \( 2 \) from both sides: \[ 7x \geq 7 \]

3. Divide by \( 7 \): \[ x \geq 1 \]

Thus, the solution to the inequality is \( x \geq 1 \).

Therefore, the correct answer is C. \( x \geq 1 \).