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:
\[ x > 2 \]