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

Options

A. `-4`
B. 3
C. `9/8`
D. `-2`

Answer

To solve the equation \((5x - 3)/(2x + 3) = 1/2\), we will follow these steps:

### Step 1: Cross Multiply
We start by cross-multiplying to eliminate the fractions. This gives us:
\[ 2 \cdot (5x - 3) = 1 \cdot (2x + 3) \]

### Step 2: Distribute
Now, we distribute the numbers on both sides:
\[ 10x - 6 = 2x + 3 \]

### Step 3: Move x Terms to One Side
Next, we want to get all the \(x\) terms on one side and the constant terms on the other side. We can subtract \(2x\) from both sides:
\[ 10x - 2x - 6 = 3 \]
This simplifies to:
\[ 8x - 6 = 3 \]

### Step 4: Move Constant Terms to the Other Side
Now, we will add \(6\) to both sides to isolate the \(x\) term:
\[ 8x = 3 + 6 \]
This simplifies to:
\[ 8x = 9 \]

### Step 5: Solve for x
Finally, we divide both sides by \(8\) to solve for \(x\):
\[ x = \frac{9}{8} \]

### Final Answer
Thus, the solution for \(x\) is:
\[ x = \frac{9}{8} \]

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