To simplify the expression \( \frac{3}{4} + \frac{1}{2}x + x - \frac{1}{4} \), we can combine like terms. Let's break it down step by step.
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Combine the constant terms: \[ \frac{3}{4} - \frac{1}{4} = \frac{3 - 1}{4} = \frac{2}{4} = \frac{1}{2} \]
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Combine the \( x \) terms: The \( x \) term is \( \frac{1}{2}x + x \). Recall that \( x \) can be written as \( \frac{2}{2}x \) to have a common denominator: \[ \frac{1}{2}x + \frac{2}{2}x = \frac{1 + 2}{2}x = \frac{3}{2}x \]
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Putting it all together: Now, we can combine the results: \[ \frac{1}{2} + \frac{3}{2}x \]
So, the simplified expression is: \[ \frac{3}{2}x + \frac{1}{2} \]