Solve for `x : (3x -2)/(5x + 7) = (1)/(12)`

Options

A. `-4`
B. 3
C. 1
D. `-2`

Explanation

To solve the equation \(\frac{3x - 2}{5x + 7} = \frac{1}{12}\), we will follow these steps:

### Step 1: Cross-Multiply
We start by cross-multiplying to eliminate the fractions. This means we multiply the numerator of the left fraction by the denominator of the right fraction and set it equal to the numerator of the right fraction multiplied by the denominator of the left fraction.

\[ 12(3x - 2) = 1(5x + 7) \]

### Step 2: Distribute
Next, we distribute the numbers outside the parentheses on both sides of the equation.

\[ 36x - 24 = 5x + 7 \]

### Step 3: Move all terms involving \(x\) to one side
Now, we will move all terms involving \(x\) to one side and constant terms to the other side. We can do this by subtracting \(5x\) from both sides.

\[ 36x - 5x - 24 = 7 \]

This simplifies to:

\[ 31x - 24 = 7 \]

### Step 4: Move constant terms to the other side
Next, we add \(24\) to both sides to isolate the term with \(x\).

\[ 31x = 7 + 24 \]

This simplifies to:

\[ 31x = 31 \]

### Step 5: Solve for \(x\)
Finally, we divide both sides by \(31\) to solve for \(x\).

\[ x = \frac{31}{31} \]

This simplifies to:

\[ x = 1 \]

### Final Answer
Thus, the solution to the equation is:

\[ \boxed{1} \]

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