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

Options

A. 9
B. `3(1)/(2)`
C. 18
D. 38

Answer

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:

\[ m = 18 \]