Question

Which answer gives all the values of x for which the inequality
3x + 2≥9 - 4x is true? (1 point)
• x=1
0 x≤1
x≥1
0 x> 1

Answer 1

To solve the inequality \(3x + 2 \geq 9 - 4x\), we first rearrange it to isolate \(x\).

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

2. Subtract \(2\) from both sides:
\[
7x \geq 9 - 2
\]
\[
7x \geq 7
\]

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

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

Based on the options provided:
- \(x = 1\) (not correct, it's a single value)
- \(0\) \(x \leq 1\) (not correct)
- \(x \geq 1\) (correct)
- \(0\) \(x > 1\) (not correct)

The correct answer is **\(x \geq 1\)**.