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:
- \( \frac{1}{5}(2x - 7y) \)
- \( 5(2x - 7y) \)
- \( \frac{1}{5}(7x + 2y) \)
- \( 5(7x + 2y) \)
The first option, \( \frac{1}{5}(2x - 7y) \), is equivalent to our original expression.
Thus, the correct answer is:
\[ \frac{1}{5}(2x - 7y) \]
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