Which answer gives all the values of x

Question

for which the inequality 3x+2≥9−4x
is true?(1 point)
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
x equals 1
Remaining Attempts : 3
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Answer 1

To solve the inequality \( 3x + 2 \geq 9 - 4x \), we can start by isolating \( x \).

1. First, we can add \( 4x \) to both sides: \[ 3x + 4x + 2 \geq 9 \]

2. This simplifies to: \[ 7x + 2 \geq 9 \]

3. Next, subtract \( 2 \) from both sides: \[ 7x \geq 7 \]

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

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

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