Let's solve the equation step by step:

Given equation:

$10 + x = 2x - 2$

Step 1: Move $x$ to one side

Subtract $x$ from both sides to get: $10 = 2x - x - 2$ $10 = x - 2$

Step 2: Move the constant to the other side

Add 2 to both sides to isolate $x$: $10 + 2 = x$ $12 = x$

So, the solution is $x = 12$.

Substitution:

To verify, substitute $x = 12$ back into the original equation: $10 + 12 = 2(12) - 2$ $22 = 24 - 2$ $22 = 22$

Both sides are equal, so the solution is correct.

Would you like any further details or explanations?

Here are 5 related questions to expand on this:

1. How would the solution change if the equation were $10 + x = 3x - 2$?
2. What would happen if there were fractions involved, such as $\frac{10}{2} + x = 2x - 2$?
3. Can you solve the equation $10 + 2x = 4x - 4$?
4. How does solving for $x$ change if the equation had more terms like $10 + x^2 = 2x - 2$?
5. What happens when you substitute $x = 12$ into a different equation, such as $3x - 5 = 0$?

Tip: Always verify your solution by substituting it back into the original equation to ensure both sides are equal.