Let's solve the equation step by step:

The given equation is:

\[
-2(-x + 3) + 4x + 2 = 2
\]

### Step 1: Distribute the \(-2\) to both terms inside the parentheses.
\[
-2(-x) + (-2)(3) + 4x + 2 = 2
\]
This simplifies to:
\[
2x - 6 + 4x + 2 = 2
\]

### Step 2: Combine like terms on the left side.
\[
(2x + 4x) + (-6 + 2) = 2
\]
\[
6x - 4 = 2
\]

### Step 3: Add 4 to both sides to isolate the term with \(x\).
\[
6x - 4 + 4 = 2 + 4
\]
\[
6x = 6
\]

### Step 4: Divide both sides by 6.
\[
x = \frac{6}{6}
\]
\[
x = 1
\]

### Final Answer:
\[
x = 1
\]

Would you like more details or have any other questions?

Here are 5 related questions:
1. How do you solve a linear equation with multiple steps?
2. What is the distributive property, and how is it applied?
3. How do you combine like terms in an algebraic expression?
4. How do you check if a solution to an equation is correct?
5. Can linear equations have more than one solution?

**Tip:** Always double-check your solution by substituting it back into the original equation!

Step-by-step solution to solve the linear equation -2(-x + 3) + 4x + 2 = 2. Learn how to apply the distributive property, combine like terms, and solve for x. This guide is ideal for students in Grades 7-9.

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