1/2 (x+4) + 1/4 (4x-2)

1 answer

To simplify the expression \( \frac{1}{2}(x+4) + \frac{1}{4}(4x-2) \), follow these steps:

1. Distribute each fraction to both terms inside the parentheses.

\[
\frac{1}{2} \cdot x + \frac{1}{2} \cdot 4 + \frac{1}{4} \cdot 4x - \frac{1}{4} \cdot 2
\]

2. Perform the multiplication.

\[
\frac{1}{2}x + 2 + x - \frac{1}{2}
\]

3. Combine like terms.

\[
\frac{1}{2}x + x + 2 - \frac{1}{2}
\]

\[
\frac{2}{2}x + \frac{2}{2}x + 2 - \frac{1}{2}
\]

4. Add the x terms together.

\[
\frac{4}{2}x + \frac{3}{2}
\]

5. Simplify the fraction \( \frac{4}{2} \) to get 2.

\[
2x + \frac{3}{2}
\]

To summarize, the simplified form of the expression \( \frac{1}{2}(x+4) + \frac{1}{4}(4x-2) \) is \( 2x + \frac{3}{2} \).