To solve the inequality \( \frac{4}{7}x - \frac{2}{7} > \frac{5}{7} \), follow these steps:
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Get rid of the fractions by multiplying all terms by 7 (which is a positive number, so the direction of the inequality does not change):
\[ 7 \left( \frac{4}{7}x \right) - 7 \left( \frac{2}{7} \right) > 7 \left( \frac{5}{7} \right) \]
This simplifies to:
\[ 4x - 2 > 5 \]
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Add 2 to both sides of the inequality:
\[ 4x - 2 + 2 > 5 + 2 \]
This simplifies to:
\[ 4x > 7 \]
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Divide by 4:
\[ x > \frac{7}{4} \]
So the solution to the inequality is:
\[ x > \frac{7}{4} \]
Or in decimal form:
\[ x > 1.75 \]