Solve for x: 4x + one half(2x + 4) > 12

Question

x > fourteen fifths
x < fourteen fifths
x > 2
x < 2

Answer 1

To solve the inequality $4x+\frac{1}{2}(2x+4)>12$, we first need to simplify the expression on the left-hand side.

1. Distribute the $\frac{1}{2}$ inside the parenthesis:
$$\frac{1}{2}(2x+4)=\frac{1}{2}(2x)+\frac{1}{2}(4)=x+2$$

2. Substitute back into the original inequality:
$$4x+x+2>12$$
Combine like terms:
$$5x+2>12$$

3. Subtract 2 from both sides to isolate the term with the variable:
$$5x>10$$

4. Divide each side by 5 to solve for $x$:
$$x>2$$

Thus, the solution to the inequality is $x>2$.

Therefore, the correct answer is:
$$x>2$$