Question

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

Answer 1

Wrong the answer should be a mixed number

Answer 2

To add the expression \( \frac{1}{2}(x+4) + \frac{1}{4}(4x-2) \), we will first distribute the fractions:

1. Distributing \( \frac{1}{2} \) into \( (x+4) \):

\[
\frac{1}{2}(x+4) = \frac{1}{2}x + \frac{1}{2} \cdot 4 = \frac{1}{2}x + 2
\]

2. Distributing \( \frac{1}{4} \) into \( (4x-2) \):

\[
\frac{1}{4}(4x-2) = \frac{1}{4} \cdot 4x - \frac{1}{4} \cdot 2 = x - \frac{1}{2}
\]

3. Now, we add these two results together:

\[
\left(\frac{1}{2}x + 2\right) + \left(x - \frac{1}{2}\right)
\]

4. 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 constants \( 2 \) and \( -\frac{1}{2} \):

\[
2 - \frac{1}{2} = 2 - 0.5 = 1.5 = \frac{3}{2}
\]

5. Putting it all together, we have:

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

6. We can factor out \( \frac{3}{2} \):

\[
\frac{3}{2}(x + 1)
\]

The final answer in mixed number form is:

\[
\frac{3}{2}(x + 1) = \frac{3}{2}x + \frac{3}{2}
\]

So the answer is \( \frac{3}{2}x + 1 \frac{1}{2} \) (as a mixed number).