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

Options

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

Answer

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

### Step 1: Cross-Multiply
Cross-multiply to eliminate the fractions:
\[ 3(3x + 5) = 1(2x + 1) \]

### Step 2: Distribute
Distribute the numbers on both sides:
\[ 9x + 15 = 2x + 1 \]

### Step 3: Move \(x\) Terms to One Side
Subtract \(2x\) from both sides to get all \(x\) terms on one side:
\[ 9x - 2x + 15 = 1 \]
This simplifies to:
\[ 7x + 15 = 1 \]

### Step 4: Move Constant Terms to the Other Side
Subtract \(15\) from both sides:
\[ 7x = 1 - 15 \]
This simplifies to:
\[ 7x = -14 \]

### Step 5: Solve for \(x\)
Divide both sides by \(7\):
\[ x = \frac{-14}{7} \]
This simplifies to:
\[ x = -2 \]

### Final Answer
The solution to the equation is:
\[ \boxed{-2} \]

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