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

Question

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

Answer 1

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.