Let's solve the equation step by step.
Given the equation: \[ \frac{4}{5}x - 5 = \frac{1}{4} \]
- Add 5 to both sides: \[ \frac{4}{5}x = \frac{1}{4} + 5 \]
To add \(5\), we can convert it to a fraction with a common denominator: \[ 5 = \frac{5 \times 4}{1 \times 4} = \frac{20}{4} \]
Now we can add: \[ \frac{1}{4} + \frac{20}{4} = \frac{21}{4} \]
So we have: \[ \frac{4}{5}x = \frac{21}{4} \]
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Multiply both sides by \(5\) to eliminate the fraction in front of \(x\): \[ 4x = \frac{21}{4} \cdot 5 \] \[ 4x = \frac{21 \times 5}{4} = \frac{105}{4} \]
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Now we can write the equation without fractions as: \[ 45x = 105 \]
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Now, divide both sides by \(4\) to solve for \(x\): \[ x = \frac{105}{4} \div \frac{4}{5} \]
Dividing by a fraction is the same as multiplying by its reciprocal: \[ x = \frac{105}{4} \cdot \frac{5}{4} = \frac{105 \times 5}{4 \times 4} = \frac{525}{16} \]
So the completed solution is:
- \( \frac{4}{5}x = \frac{21}{4} \) (from adding 5)
- \( 45x = 105 \) (when multiplying both sides by \(5\))
- \( x = \frac{525}{16} \) (when dividing both sides by \( \frac{4}{5} \))
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