Simplify: `x^2-3x+5-1/2(3x^2-5x+7)`

Explanation

To simplify the expression \( x^2 - 3x + 5 - \frac{1}{2}(3x^2 - 5x + 7) \), we will follow these steps:

### Step 1: Distribute the \(-\frac{1}{2}\) to the terms inside the parentheses
We start by distributing \(-\frac{1}{2}\) to each term in the expression \(3x^2 - 5x + 7\):

\[ -\frac{1}{2}(3x^2) + \frac{1}{2}(5x) - \frac{1}{2}(7) = -\frac{3}{2}x^2 + \frac{5}{2}x - \frac{7}{2} \]
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