To solve the equation \( \frac{4}{5}x - 5 = \frac{1}{4} \), we can follow the steps you've outlined.
Let's solve it step-by-step.
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Add 5 to both sides of the equation: \[ \frac{4}{5}x - 5 + 5 = \frac{1}{4} + 5 \] This simplifies to: \[ \frac{4}{5}x = \frac{1}{4} + 5 \] To add \( 5 \) (which can be expressed as \( \frac{20}{4} \)) to \( \frac{1}{4} \): \[ \frac{1}{4} + \frac{20}{4} = \frac{21}{4} \] So, we have: \[ \frac{4}{5}x = \frac{21}{4} \]
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Now to find \( x \): Divide both sides by \( \frac{4}{5} \): \[ x = \frac{21/4}{4/5} \] To divide by a fraction, we multiply by its reciprocal: \[ x = \frac{21}{4} \times \frac{5}{4} = \frac{21 \times 5}{4 \times 4} = \frac{105}{16} \]
Finally, the completed steps are:
- \( \frac{4}{5}x = \frac{21}{4} \)
- \( x = \frac{105}{16} \)
So, the answers are:
- \( \frac{4}{5}x = \frac{21}{4} \)
- \( x = \frac{105}{16} \)