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 $3x+2\ge 9-4x$, we can first isolate $x$. Here are the steps:

1. Add $4x$ to both sides: $$3x+4x+2\ge 9$$ This simplifies to: $$7x+2\ge 9$$

2. Subtract $2$ from both sides: $$7x\ge 7$$

3. Divide by $7$: $$x\ge 1$$

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

Therefore, the correct answer is C. $x\ge 1$.