To solve the equation \( \frac{4}{5}x - 5 = \frac{1}{4} \), we will complete the steps.
Step 1: Add 5 to both sides of the equation.
\[ \frac{4}{5}x - 5 + 5 = \frac{1}{4} + 5 \]
This simplifies to:
\[ \frac{4}{5}x = \frac{1}{4} + 5 \]
Now, to add \( \frac{1}{4} + 5 \), we write 5 as a fraction:
\[ 5 = \frac{20}{4} \]
So:
\[ \frac{1}{4} + \frac{20}{4} = \frac{21}{4} \]
Thus, we have:
\[ \frac{4}{5}x = \frac{21}{4} \]
Step 2: Divide both sides of the equation by \( \frac{4}{5} \).
To do this, we can multiply by the reciprocal:
\[ x = \frac{21}{4} \div \frac{4}{5} = \frac{21}{4} \cdot \frac{5}{4} = \frac{21 \cdot 5}{4 \cdot 4} = \frac{105}{16} \]
Summarizing:
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After adding 5 to both sides, we find: \[ \frac{4}{5}x = \frac{21}{4} \]
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After dividing by \( \frac{4}{5} \), we conclude: \[ x = \frac{105}{16} \]
So the final answers are:
- For \( \frac{4}{5}x = \): \( \frac{21}{4} \)
- For \( x = \): \( \frac{105}{16} \)
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