To add the expressions \( \frac{1}{2} (x + 4) \) and \( \frac{1}{4} (4x - 2) \), we can follow these steps:
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Distribute the terms in each expression: \[ \frac{1}{2}(x + 4) = \frac{1}{2}x + \frac{1}{2} \cdot 4 = \frac{1}{2}x + 2 \] \[ \frac{1}{4}(4x - 2) = \frac{1}{4} \cdot 4x - \frac{1}{4} \cdot 2 = x - \frac{1}{2} \]
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Now, combine the two results: \[ \left( \frac{1}{2}x + 2 \right) + \left( x - \frac{1}{2} \right) \]
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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 \( -\frac{1}{2} \): \[ 2 - \frac{1}{2} = \frac{4}{2} - \frac{1}{2} = \frac{3}{2} \]
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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!