To solve the equation \(6x - 2 = x + 13\), follow these steps:

1. First, move all terms involving \(x\) to one side of the equation:
\[
6x - x = 13 + 2
\]
\[
5x = 15
\]

2. Now, solve for \(x\) by dividing both sides by 5:
\[
x = \frac{15}{5}
\]
\[
x = 3
\]

The solution is \(x = 3\).

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. What happens if we modify the constant in the equation, for example, \(6x - 2 = x + 15\)?
2. How would the solution change if the equation were \(6x + 2 = x + 13\)?
3. Can you solve \(6x - 2 = 2x + 13\)?
4. How do you solve an equation where \(x\) appears on both sides with coefficients, like \(7x - 3 = 4x + 5\)?
5. How do we solve for \(x\) when there's a fraction, e.g., \(6x - 2 = \frac{1}{2}x + 13\)?

**Tip:** Always combine like terms and simplify the equation step by step for clarity.

Learn how to solve the linear equation 6x - 2 = x + 13 with a detailed step-by-step solution. This problem covers fundamental algebraic concepts, including combining like terms and solving for variables. Suitable for students in Grades 6-8.

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