Reduce to linear form \(\frac{5x + 1}{2x} = \frac{5}{4}\)
Equation Reduction Steps
The goal is to simplify the given fractional equation into a linear form (\(ax + b = 0\)).
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Start with the given equation:
\(\frac{5x + 1}{2x} = \frac{5}{4}\)
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Cross-multiply: Multiply the numerator of the left side by the denominator of the right side, and the numerator of the right side by the denominator of the left side.
\(4 \times (5x + 1) = 5 \times (2x)\)
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Expand both sides: Distribute the constants.
\(20x + 4 = 10x\)
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Rearrange into linear form: Move all terms to one side to set the equation equal to zero. Subtract \(10x\) from both sides.
\(20x - 10x + 4 = 0\)
\(10x + 4 = 0\)
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Simplify the linear equation: Divide by the greatest common divisor (which is 2) to get the simplest linear form.
\(\frac{10x}{2} + \frac{4}{2} = \frac{0}{2}\)
\(5x + 2 = 0\)
This final equation, \(5x + 2 = 0\), is the linear form of the original fractional equation and matches Option B.
Similar Questions
- For what value of K is the equation \(\frac{0.009}{K} = 0.1\) true?
- Arnab buys 9 oranges and 8 bananas for ₹276. When the cost of an orange is decreased by 10% and that of a banana remains the same, then the cost of 5 oranges and 10 bananas is ₹210. What is the original cost of 4 oranges and 3 bananas?
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Important Questions from Algebric Equations
- For what value of K is the equation \(\frac{0.009}{K} = 0.1\) true?
- Arnab buys 9 oranges and 8 bananas for ₹276. When the cost of an orange is decreased by 10% and that of a banana remains the same, then the cost of 5 oranges and 10 bananas is ₹210. What is the original cost of 4 oranges and 3 bananas?
- Find the value of x satisfying: $5(5x^2 - 5) - 5(5x^2 + 7x - 2) = 14$
- The product of two positive numbers is 3645. If the first number is five times the second number, then the sum of the two numbers is:
- The product of two positive numbers is 80. If the first number is five times of the second number, then the sum of the two numbers is:
