Question

Add: 1/2 (x+4) + 1/4 (4x-2). Answer should be in mixed number form.
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Answer 1

wrong needs to be mixed number

Answer 2

To add the two fractions \( \frac{1}{2}(x + 4) + \frac{1}{4}(4x - 2) \), we'll first simplify each term.

1. Simplify \( \frac{1}{2}(x + 4) \):
\[
\frac{1}{2}(x + 4) = \frac{x + 4}{2}
\]

2. Simplify \( \frac{1}{4}(4x - 2) \):
\[
\frac{1}{4}(4x - 2) = \frac{4x - 2}{4}
\]
We can further simplify \( \frac{4x - 2}{4} = x - \frac{1}{2} \).

Now we can combine the two terms:
\[
\frac{x + 4}{2} + \left( x - \frac{1}{2} \right)
\]

To add these, we need a common denominator. The common denominator is 2:
\[
x - \frac{1}{2} = \frac{2x}{2} - \frac{1}{2} = \frac{2x - 1}{2}
\]

Now add:
\[
\frac{x + 4}{2} + \frac{2x - 1}{2} = \frac{x + 4 + 2x - 1}{2} = \frac{3x + 3}{2}
\]

This can be factored further:
\[
\frac{3(x + 1)}{2}
\]

Now we can express this in mixed number form if necessary. Since \( 3(x+1) \) is a polynomial, to convert this to mixed number format would only apply if we had a fractional component. Here, we can leave it as a fraction.

Thus, the final answer is:
\[
\frac{3(x + 1)}{2}
\]

This expression does not convert neatly into a mixed number, but is simplified fully. If you need it evaluated for a specific value of \( x \), please provide that value!