Let's solve the equation step by step.
Starting with the equation: \[ \frac{4}{5}x - 5 = \frac{1}{4} \]
Step 1: Add 5 to both sides.
To isolate the term with \( x \), we add \( 5 \) to both sides: \[ \frac{4}{5}x = \frac{1}{4} + 5 \]
To add \( 5 \), we convert it to a fraction. Since \( 5 = \frac{5 \times 4}{4} = \frac{20}{4} \), we have: \[ \frac{1}{4} + \frac{20}{4} = \frac{21}{4} \]
So now we have: \[ \frac{4}{5}x = \frac{21}{4} \]
Step 2: Divide both sides by \( \frac{4}{5} \).
To solve for \( x \), we divide both sides by \( \frac{4}{5} \): \[ x = \frac{\frac{21}{4}}{\frac{4}{5}} \]
Dividing by a fraction is the same as multiplying by its reciprocal: \[ x = \frac{21}{4} \times \frac{5}{4} = \frac{21 \times 5}{4 \times 4} = \frac{105}{16} \]
Putting it all together, we get:
- \( \frac{4}{5}x = \frac{21}{4} \)
- \( x = \frac{105}{16} \)
So the final answers are:
- For \( \frac{4}{5}x = \): \(\frac{21}{4}\)
- For \( x = \): \(\frac{105}{16}\)