Which answer gives all the values of x for which the inequality 3x+2≥9−4x is true?(1 point)

Question

Responses

x≤1
x less-than-or-equal-to 1

x≥1
x greater-than-or-equal-to 1

x>1
x greater than 1

x=1

Answer 1

To solve the inequality \(3x + 2 \geq 9 - 4x\), we can start by moving all terms involving \(x\) to one side and the constant terms to the other side:

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

2. Next, subtract \(2\) from both sides: \[ 7x \geq 9 - 2 \] This simplifies to: \[ 7x \geq 7 \]

3. Finally, divide both sides by \(7\): \[ x \geq 1 \]

Thus, the solution to the inequality \(3x + 2 \geq 9 - 4x\) is: \[ x \geq 1 \]

The correct answer from the choices given is: x ≥ 1 (x greater-than-or-equal-to 1).