(10+x)=2x-2 and after findings substitute

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.

The query submitted by the user: (10 + x) = 2x - 2 and after findings substitute

Learn how to solve the linear equation 10 + x = 2x - 2 with a detailed step-by-step explanation. This problem demonstrates key algebraic techniques, including isolating variables and verifying solutions. Suitable for students in Grades 6-8.

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