To solve the inequality \( \frac{x}{4} + 7 \leq \frac{5}{7} \), follow these steps:
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Isolate the term with \( x \):
\[ \frac{x}{4} \leq \frac{5}{7} - 7 \]
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Convert 7 to a fraction with a denominator of 7:
\[ 7 = \frac{49}{7} \]
Therefore,
\[ \frac{5}{7} - 7 = \frac{5}{7} - \frac{49}{7} = \frac{5 - 49}{7} = \frac{-44}{7} \]
Now the inequality is:
\[ \frac{x}{4} \leq \frac{-44}{7} \]
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Multiply both sides by 4 to eliminate the fraction with \( x \). Remember to maintain the inequality direction (multiplying by a positive number):
\[ x \leq 4 \cdot \frac{-44}{7} = \frac{-176}{7} \]
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State the solution:
The solution to the inequality \( \frac{x}{4} + 7 \leq \frac{5}{7} \) is:
\[ x \leq \frac{-176}{7} \]
This means that \( x \) can take any value up to and including \( \frac{-176}{7} \).