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