Let's solve the equation step by step and fill in the blanks with the correct numbers.
Given equation: \[ \frac{4}{5}x - 5 = \frac{1}{4} \]
Step 1: Add 5 to both sides of the equation
To isolate the term with \(x\), we need to add \(5\) to both sides.
Adding \(5\) (which can be written as \(\frac{20}{4}\) for common denominators), we have: \[ \frac{4}{5}x = \frac{1}{4} + 5 \]
Calculating the right side: \[ 5 = \frac{20}{4} \]
Now add: \[ \frac{1}{4} + \frac{20}{4} = \frac{21}{4} \]
Thus, the equation is: \[ \frac{4}{5}x = \frac{21}{4} \]
Step 2: Solve for \(x\)
To find \(x\), we will multiply both sides by the reciprocal of \(\frac{4}{5}\), which is \(\frac{5}{4}\): \[ x = \frac{21}{4} \cdot \frac{5}{4} \]
Calculating the right side gives: \[ x = \frac{21 \cdot 5}{4 \cdot 4} = \frac{105}{16} \]
Filling in the blanks:
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From \(\frac{4}{5}x = \frac{21}{4}\), we note that the answer to the first blank is: \[ \frac{21}{4} \]
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For \(x\), we found: \[ x = \frac{105}{16} \]
Final Answers:
- \(\frac{4}{5}x = \frac{21}{4}\)
- \(x = \frac{105}{16}\)
1 answer