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

Answer

To solve the equation \(\frac{2x+1}{7x-2}=\frac{3}{5}\), we will use cross-multiplication. Here are the steps:

### Step-by-Step Solution:

**Step 1: Cross-Multiply**
We start by cross-multiplying the fractions:
\[ 5(2x + 1) = 3(7x - 2) \]

**Step 2: Distribute**
Now, we distribute the constants on both sides:
\[ 5 \cdot 2x + 5 \cdot 1 = 3 \cdot 7x - 3 \cdot 2 \]
This simplifies to:
\[ 10x + 5 = 21x - 6 \]

**Step 3: Move all terms involving \(x\) to one side**
Next, we will move all terms involving \(x\) to one side and constant terms to the other side. We can do this by subtracting \(10x\) from both sides:
\[ 5 + 6 = 21x - 10x \]
This simplifies to:
\[ 11 = 11x \]

**Step 4: Solve for \(x\)**
Now, we can solve for \(x\) by dividing both sides by 11:
\[ x = \frac{11}{11} \]
This simplifies to:
\[ x = 1 \]

### Final Answer:
The solution to the equation is:
\[ x = 1 \]