Let's solve the equation \( 22x - 2x + 2 = 12 \).

### Step 1: Simplify the equation
First, combine like terms on the left-hand side:

\[
22x - 2x = 20x
\]

So the equation simplifies to:

\[
20x + 2 = 12
\]

### Step 2: Isolate the variable term
Next, subtract 2 from both sides to isolate the term with \(x\):

\[
20x = 12 - 2
\]

\[
20x = 10
\]

### Step 3: Solve for \(x\)
Now, divide both sides by 20 to solve for \(x\):

\[
x = \frac{10}{20}
\]

\[
x = \frac{1}{2}
\]

### Solution
The solution to the equation is \( x = \frac{1}{2} \).

Would you like more details, or do you have any questions?

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Here are 8 related questions to consider:
1. What happens if the equation had been \( 22x - 2x + 2 = 0 \)?
2. How would the solution change if there were different coefficients for \(x\)?
3. What if the equation was quadratic instead of linear?
4. How can you verify the solution \( x = \frac{1}{2} \) is correct?
5. What if the constant term on the right side was negative?
6. How would the equation change if we introduced a square root?
7. What if \(x\) was in the denominator?
8. How does this problem relate to systems of linear equations?

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

Learn how to solve the linear equation 22x - 2x + 2 = 12 with a detailed step-by-step solution. This problem covers basic algebraic concepts, including simplifying equations and isolating variables. Suitable for students in Grades 6-8.

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