To solve the equation $13x + 1 = 9x + 37$, let's follow these steps:

1. Subtract $9x$ from both sides to move the $x$-terms to one side: $13x - 9x + 1 = 37$ Simplifying: $4x + 1 = 37$

2. Subtract 1 from both sides to isolate the term with $x$: $4x = 37 - 1$ Simplifying: $4x = 36$

3. Divide both sides by 4 to solve for $x$: $x = \frac{36}{4}$ Simplifying: $x = 9$

Thus, the solution is $x = 9$.

Would you like more details on the steps? Or do you have any other questions?

Here are 5 related questions:

1. What happens if you change the constants in the equation?
2. How would you solve $13x + 1 = 9x + 5$?
3. What is the difference between solving an equation with $x$ on both sides versus one side?
4. Can you solve $5x - 3 = 2x + 9$?
5. How do you handle equations with fractions?

Tip: Always try to move all variables to one side of the equation and constants to the other for easier solving.