Prove that 3(5-2x)=7x+6 has a unique rational solution.

1. Start with the equation:
3(5 - 2x) = 7x + 6

2. Distribute the 3 on the left side:
15 - 6x = 7x + 6

3. Rearrange the equation to bring all terms involving \(x\) to one side:
-6x - 7x = 6 - 15

4. Combine like terms:
-13x = -9

5. Solve for \(x\) by dividing both sides by \(-13\):
x = \frac{-9}{-13}

6. Simplify the expression:
x = \frac{9}{13}

Thus, the unique rational solution is \( x = \frac{9}{13} \).