To solve the equation \( \frac{1}{4}(2x - 4) = 14 \) through distribution, you need to distribute \( \frac{1}{4} \) to both terms inside the parentheses.
Here's how it is done step by step:
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Distribute \( \frac{1}{4} \): \[ \frac{1}{4}(2x) - \frac{1}{4}(4) = 14 \]
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Perform the multiplications: \[ \frac{1}{4} \cdot 2x = \frac{2}{4}x = \frac{1}{2}x \] \[ \frac{1}{4} \cdot 4 = 1 \]
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Substitute back into the equation: \[ \frac{1}{2}x - 1 = 14 \]
So, after distributing, the result is: \[ \frac{1}{2}x - 1 = 14 \]
The first option you provided — \( \frac{1}{2}x - 1 = 14 \) — is the correct distribution result. The other options are not correct representations of the equation after distributing.