https://file.aiquickdraw.com/mathbot/file/1728449822848xvi84wwu.jpg

The equation in the image is:

\[
-2 + 2x - 2x = 6 + 2x
\]

Let's solve this step by step:

1. First, simplify both sides of the equation.
   On the left-hand side, \( 2x - 2x = 0 \), so we are left with:
   \[
   -2 = 6 + 2x
   \]

2. Next, subtract 6 from both sides to isolate the term with \( x \):
   \[
   -2 - 6 = 2x
   \]
   Simplifying:
   \[
   -8 = 2x
   \]

3. Finally, divide both sides by 2 to solve for \( x \):
   \[
   x = \frac{-8}{2} = -4
   \]

Thus, the solution is \( x = -4 \).

Would you like more details or have any questions?

Here are 5 related questions you can explore:
1. What happens if you have an equation where variables don't cancel out like in step 1?
2. How do you solve equations where \( x \) appears on both sides without simplifying first?
3. What types of equations cannot be simplified as easily as this one?
4. What methods can be used if the equation involves fractions?
5. How do you check if your solution for \( x \) is correct?

**Tip:** Always simplify each side of an equation as much as possible before solving!

Learn how to solve the linear equation -2 + 2x - 2x = 6 + 2x with a detailed step-by-step solution. This problem covers key algebraic concepts, such as simplifying and solving linear equations. Suitable for students in Grades 7-9.

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