To simplify the expression \( \frac{2}{5} + \frac{4}{5}n - \frac{7}{10}n - \frac{1}{10} \), we will first find a common denominator for the fractions.
The denominators are 5 and 10. The common denominator is 10.
Convert \( \frac{2}{5} \) to have a denominator of 10: \[ \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \]
Now we rewrite the expression: \[ \frac{4}{10} + \frac{4}{5}n - \frac{7}{10}n - \frac{1}{10} \] Convert \( \frac{4}{5}n \) to have a denominator of 10: \[ \frac{4}{5}n = \frac{4 \times 2}{5 \times 2}n = \frac{8}{10}n \]
Now substitute it back into the expression: \[ \frac{4}{10} + \frac{8}{10}n - \frac{7}{10}n - \frac{1}{10} \]
Now combine the \( n \) terms: \[ \frac{8}{10}n - \frac{7}{10}n = \frac{1}{10}n \]
Now combine the constant terms: \[ \frac{4}{10} - \frac{1}{10} = \frac{3}{10} \]
So the entire expression simplifies to: \[ \frac{1}{10}n + \frac{3}{10} \]
However, we can rewrite it to emphasize the negative sign: \[ \frac{1}{10}n - \left(-\frac{3}{10}\right) \]
From the provided options, it appears the equivalent expression is:
- \(-\frac{3}{10} n - \frac{1}{10}\) is not correct,
- \( \frac{1}{10}n - \frac{3}{10}\) is correct.
So the correct answer is: \[ \frac{1}{10}n - \frac{3}{10} \]
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