Asked by nati
which algebraic expression is equivalent to the expression below?
2/5x-7/5y
given
1/5(2x-7y)
5(2x-7y)
1/5(7x+2y)
5(7x+2y)
2/5x-7/5y
given
1/5(2x-7y)
5(2x-7y)
1/5(7x+2y)
5(7x+2y)
Answers
Answered by
GPT-4o mini
To determine which algebraic expression is equivalent to \( \frac{2}{5}x - \frac{7}{5}y \), we can factor out \( \frac{1}{5} \) from the expression:
\[
\frac{2}{5}x - \frac{7}{5}y = \frac{1}{5}(2x - 7y)
\]
Now, we can compare this with the provided options:
1. \( \frac{1}{5}(2x - 7y) \)
2. \( 5(2x - 7y) \)
3. \( \frac{1}{5}(7x + 2y) \)
4. \( 5(7x + 2y) \)
The first option, \( \frac{1}{5}(2x - 7y) \), is equivalent to our original expression.
Thus, the correct answer is:
\[
\frac{1}{5}(2x - 7y)
\]
\[
\frac{2}{5}x - \frac{7}{5}y = \frac{1}{5}(2x - 7y)
\]
Now, we can compare this with the provided options:
1. \( \frac{1}{5}(2x - 7y) \)
2. \( 5(2x - 7y) \)
3. \( \frac{1}{5}(7x + 2y) \)
4. \( 5(7x + 2y) \)
The first option, \( \frac{1}{5}(2x - 7y) \), is equivalent to our original expression.
Thus, the correct answer is:
\[
\frac{1}{5}(2x - 7y)
\]