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The value of m that satisfies the equati...

The value of m that satisfies the equation `(7)/(4m-2) = (5)/(3m-4)` is :

A

9

B

`3(1)/(2)`

C

18

D

38

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \(\frac{7}{4m-2} = \frac{5}{3m-4}\), we will follow these steps: ### Step 1: Cross-Multiply We start by cross-multiplying the fractions. This means we will multiply the numerator of the first fraction by the denominator of the second fraction and set it equal to the numerator of the second fraction multiplied by the denominator of the first fraction. \[ 7 \cdot (3m - 4) = 5 \cdot (4m - 2) \] ### Step 2: Distribute Next, we will distribute the numbers on both sides of the equation. \[ 21m - 28 = 20m - 10 \] ### Step 3: Move the terms involving \(m\) to one side Now, we will move all terms involving \(m\) to one side and the constant terms to the other side. We can do this by subtracting \(20m\) from both sides. \[ 21m - 20m = -10 + 28 \] ### Step 4: Simplify Now we simplify both sides of the equation. \[ m = 18 \] ### Final Answer The value of \(m\) that satisfies the equation is: \[ m = 18 \]
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Knowledge Check

  • Find the value of m that satisfy the inequation m+3sqrtm-4gt0 .

    A
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    B
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    A
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    C
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    D
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