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Solve the inequality [tex]n - \frac{3}{5} \leq -\frac{4}{7}[/tex] for [tex]n[/tex].
To solve the inequality [tex]\( n - \frac{3}{5} \leq -\frac{4}{7} \)[/tex] for [tex]\( n \)[/tex], follow these steps:
1. Isolate [tex]\( n \)[/tex]: To isolate [tex]\( n \)[/tex], we need to get rid of the term [tex]\(-\frac{3}{5}\)[/tex] on the left-hand side. We do this by adding [tex]\(\frac{3}{5}\)[/tex] to both sides of the inequality: [tex]\[
n - \frac{3}{5} + \frac{3}{5} \leq -\frac{4}{7} + \frac{3}{5}
\][/tex] Simplifies to: [tex]\[
n \leq -\frac{4}{7} + \frac{3}{5}
\][/tex]
2. Find a common denominator: To add the fractions [tex]\(-\frac{4}{7}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex], we need a common denominator. The least common multiple (LCM) of 7 and 5 is 35. So we convert the fractions: [tex]\[
-\frac{4}{7} = -\frac{4 \times 5}{7 \times 5} = -\frac{20}{35}
\][/tex] [tex]\[
\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}
\][/tex]
3. Add the fractions: [tex]\[
n \leq -\frac{20}{35} + \frac{21}{35}
\][/tex] Combine the fractions: [tex]\[
n \leq \frac{-20 + 21}{35} = \frac{1}{35}
\][/tex]
Thus, the solution to the inequality is: [tex]\[
n \leq \frac{1}{35}
\][/tex]
So, the correct answer is: [tex]\[
n \leq \frac{1}{35}
\][/tex]
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