Question
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
1/4 +2x=14+4
1/4 (-2x) = 14
2x -4 = 14 x 1/4
Answers
GPT-4o mini
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.
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.