To solve the equation \( 500 + x = 1.06x \), we need to isolate \( x \). Here are the steps:

1. Start with the equation:
   \[
   500 + x = 1.06x
   \]

2. Subtract \( x \) from both sides to get the terms involving \( x \) on one side:
   \[
   500 + x - x = 1.06x - x
   \]

3. Simplify both sides:
   \[
   500 = 0.06x
   \]

4. Divide both sides by 0.06 to solve for \( x \):
   \[
   x = \frac{500}{0.06}
   \]

5. Calculate the value of \( x \):
   \[
   x = \frac{500}{0.06} = 8333.33\overline{3}
   \]

So, the solution is \( x \approx 8333.33 \).

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

Here are 8 relative questions expanding on this information:

1. What happens if we change 1.06 to another coefficient, say 1.1?
2. How do we handle similar equations if the coefficients are negative?
3. What are the implications of solving equations with variables on both sides?
4. Can we solve this type of equation using graphical methods?
5. How do equations like these apply to real-world problems?
6. What techniques are useful for solving more complex algebraic equations?
7. How would we verify the solution \( x \) is correct?
8. What happens if there is no solution to an equation?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the linear equation 500 + x = 1.06x with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving linear equations and isolating variables. Suitable for students in Grades 7-9.

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