Let's solve the equation \(7x - 70 = 6x - 30\).

1. **Move all terms involving \(x\) to one side** of the equation by subtracting \(6x\) from both sides:
   \[
   7x - 6x - 70 = 6x - 6x - 30
   \]
   Simplifying this gives:
   \[
   x - 70 = -30
   \]

2. **Move the constant term** on the left side to the right side by adding 70 to both sides:
   \[
   x - 70 + 70 = -30 + 70
   \]
   Simplifying this gives:
   \[
   x = 40
   \]

So, the solution is \(x = 40\).

Would you like any further details or have any questions?

Here are some related questions you might find interesting:

1. What happens if we change the equation to \(8x - 80 = 6x - 30\)?
2. How would the solution change if the equation was \(7x - 70 = 6x - 100\)?
3. What is the general method to solve linear equations?
4. How do you check if the solution to a linear equation is correct?
5. How would the solution change if both sides of the equation were multiplied by a constant?

**Tip:** Always isolate the variable on one side of the equation to solve for it effectively.

Learn how to solve the linear equation 7x - 70 = 6x - 30 step-by-step with detailed explanations. This problem involves isolating the variable and applying basic algebraic operations. Suitable for students in Grades 7-9.

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