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.

Learn how to solve the linear equation 13x + 1 = 9x + 37 with a clear, step-by-step explanation. This problem focuses on key algebraic concepts, including simplifying and isolating variables, suitable for students in Grades 6-8.

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