Let's solve the equation step-by-step and fill in the gaps.
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Start with the original equation: \[ \frac{4}{5}x - 5 = \frac{1}{4} \]
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Add 5 to both sides. To do this, convert the 5 to a fraction with a denominator of 4. Thus, \(5 = \frac{20}{4}\). \[ \frac{4}{5}x = \frac{1}{4} + \frac{20}{4} \] This simplifies to: \[ \frac{4}{5}x = \frac{21}{4} \]
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To eliminate the fraction, multiply both sides by 5 to obtain: \[ 4x = \frac{21}{4} \times 5 \] This becomes: \[ 4x = \frac{105}{4} \]
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Now we can multiply both sides by 5: \[ 45x = 105 \]
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Next, divide both sides by 45: \[ x = \frac{105}{45} \]
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Reduce \(\frac{105}{45}\): Both 105 and 45 can be divided by 15: \[ x = \frac{7}{3} \]
Summing up the results:
- For \(45x =\) the answer is \(105\).
- Therefore, \(x = \frac{7}{3}\).
Final filled responses:
- \(45x = 105\)
- \(x = \frac{7}{3}\)