Let's solve the equation \(6x + 13 = 7x - 5\).

### Step 1: Move all the terms involving \(x\) to one side.
Subtract \(6x\) from both sides:

\[
6x + 13 - 6x = 7x - 5 - 6x
\]
\[
13 = x - 5
\]

### Step 2: Move the constant terms to the other side.
Add 5 to both sides:

\[
13 + 5 = x - 5 + 5
\]
\[
18 = x
\]

Thus, the solution is:
\[
x = 18
\]

Would you like any additional details or have any questions about this solution?

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Here are five related questions to expand on this concept:

1. What happens if both sides of the equation include fractions?
2. How would you solve \(7x + 8 = 3x + 20\)?
3. Can you solve \(2(3x + 4) = 5x + 12\)?
4. What steps are used to solve \(8x - 6 = 10x + 14\)?
5. How do you solve equations with variables on both sides when decimals are involved?

**Tip:** Always remember to move all the terms involving the variable to one side and constants to the other for simplicity.

Learn how to solve the linear equation 6x + 13 = 7x - 5 with a step-by-step guide. This example demonstrates algebraic techniques such as isolating variables and simplifying constants. Suitable for students in Grades 6-8.

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