Question

Add 1/2(x+4)+1/4(4x-2) and should be a mixed number phone

Answer 1

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

1. **Distribute the fractions**:
\[
\frac{1}{2}(x + 4) = \frac{1}{2}x + \frac{1}{2} \cdot 4 = \frac{1}{2}x + 2
\]

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

2. **Combine the two resulting expressions**:
\[
\left(\frac{1}{2}x + 2\right) + \left(x - \frac{1}{2}\right)
\]

3. **Combine like terms**:
- For the \( x \) terms: \( \frac{1}{2}x + x = \frac{1}{2}x + \frac{2}{2}x = \frac{3}{2}x \)
- For the constants: \( 2 - \frac{1}{2} = 2 - 0.5 = 1.5 = \frac{3}{2} \)

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

4. **Factor out \( \frac{3}{2} \)**:
\[
\frac{3}{2}(x + 1)
\]

Since you asked for a mixed number format, we note that \( \frac{3}{2} \) can be expressed as:
\[
1 \frac{1}{2}
\]

So, the overall expression in a mixed number format becomes:
\[
1 \frac{1}{2}(x + 1)
\]

Final result:
\[
1 \frac{1}{2}(x + 1)
\]