What is the result after distributing? 1/4(2x−4)=14 the answers are : 1/2x-1=14

1/4 +2x=14+4
1/4 (-2x) = 14
2x -4 = 14 x 1/4

1 answer

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:

  1. Distribute \( \frac{1}{4} \): \[ \frac{1}{4}(2x) - \frac{1}{4}(4) = 14 \]

  2. Perform the multiplications: \[ \frac{1}{4} \cdot 2x = \frac{2}{4}x = \frac{1}{2}x \] \[ \frac{1}{4} \cdot 4 = 1 \]

  3. 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.