Let's solve the equation step by step and fill in the blanks.
Starting with the equation: \[ \frac{4}{5}x - 5 = \frac{1}{4} \]
Step 1: Add 5 to both sides of the equation.
To add 5, we need to express it as a fraction with a common denominator: \[ 5 = \frac{5 \cdot 4}{4} = \frac{20}{4} \]
Now, add this to both sides: \[ \frac{4}{5}x = \frac{1}{4} + \frac{20}{4} \] \[ \frac{4}{5}x = \frac{1 + 20}{4} = \frac{21}{4} \]
So, the first blank is: \(\frac{21}{4}\)
Step 2: Divide both sides of the equation by \(\frac{4}{5}\).
Dividing by a fraction is the same as multiplying by its reciprocal: \[ x = \frac{21}{4} \div \frac{4}{5} = \frac{21}{4} \times \frac{5}{4} \]
This gives us: \[ x = \frac{21 \cdot 5}{4 \cdot 4} = \frac{105}{16} \]
So, the second blank is: \(\frac{105}{16}\)
Final Answers:
- The first blank: \(\frac{21}{4}\)
- The second blank: \(\frac{105}{16}\)
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