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 $3x+2\ge 9-4x$, we can start by isolating $x$.

1. First, we can add $4x$ to both sides: $$3x+4x+2\ge 9$$

2. This simplifies to: $$7x+2\ge 9$$

3. Next, subtract $2$ from both sides: $$7x\ge 7$$

4. Lastly, divide both sides by $7$: $$x\ge 1$$

Thus, the solution to the inequality is $x\ge 1$.

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