Question

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

Answer 1

To add the expressions \( \frac{1}{2} (x + 4) \) and \( \frac{1}{4} (4x - 2) \), we can follow these steps:

1. Distribute the terms in each expression:
\[
\frac{1}{2}(x + 4) = \frac{1}{2}x + \frac{1}{2} \cdot 4 = \frac{1}{2}x + 2
\]
\[
\frac{1}{4}(4x - 2) = \frac{1}{4} \cdot 4x - \frac{1}{4} \cdot 2 = x - \frac{1}{2}
\]

2. Now, combine the two results:
\[
\left( \frac{1}{2}x + 2 \right) + \left( x - \frac{1}{2} \right)
\]

3. Combine like terms:
- Combine \( \frac{1}{2}x \) and \( x \):
\[
\frac{1}{2}x + x = \frac{1}{2}x + \frac{2}{2}x = \frac{3}{2}x
\]
- Combine the constant terms \( 2 \) and \( -\frac{1}{2} \):
\[
2 - \frac{1}{2} = \frac{4}{2} - \frac{1}{2} = \frac{3}{2}
\]

4. Putting it all together, we have:
\[
\frac{3}{2}x + \frac{3}{2}
\]

So, the final result is:
\[
\frac{3}{2}x + \frac{3}{2}
\]

Alternatively, you can factor it as:
\[
\frac{3}{2}(x + 1)
\]
Either form is correct!