To solve the equation \( \frac{4}{5}x - 5 = \frac{1}{4} \), let's go through the steps step-by-step:
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Add 5 to both sides: \[ \frac{4}{5}x - 5 + 5 = \frac{1}{4} + 5 \] This simplifies to: \[ \frac{4}{5}x = \frac{1}{4} + 5 \] To perform the addition , we need to express 5 as a fraction with a denominator of 4: \[ 5 = \frac{20}{4} \] So: \[ \frac{1}{4} + 5 = \frac{1}{4} + \frac{20}{4} = \frac{21}{4} \] Therefore, we have: \[ \frac{4}{5}x = \frac{21}{4} \]
The correct number to complete the solution is \( \frac{21}{4} \).
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Divide both sides by \( \frac{4}{5} \): To solve for \( x \), we can write: \[ x = \frac{\frac{21}{4}}{\frac{4}{5}} \] To divide by a fraction, we multiply by its reciprocal: \[ x = \frac{21}{4} \times \frac{5}{4} = \frac{21 \times 5}{4 \times 4} = \frac{105}{16} \]
The correct number to complete the solution is \( \frac{105}{16} \).
Putting it all together:
- The first blank (after adding 5) should be \( \frac{21}{4} \).
- The second blank (after dividing by \( \frac{4}{5} \)) should be \( \frac{105}{16} \).