Let's solve the equation step by step:

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

### Step 1: Distribute the \(-2\) across \((-x + 3)\)
\[
-2(-x) + (-2)(3) + 4x + 2 = 2
\]
This simplifies to:
\[
2x - 6 + 4x + 2 = 2
\]

### Step 2: Combine like terms
\[
(2x + 4x) + (-6 + 2) = 2
\]
\[
6x - 4 = 2
\]

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

### Step 4: Divide both sides by 6 to solve for \(x\)
\[
x = \frac{6}{6}
\]
\[
x = 1
\]

So, the solution is:
\[
x = 1
\]

Would you like more details on any step? 

Here are 5 related questions for further practice:
1. Solve: \(-3(x - 2) + 5x + 7 = 3\)
2. Solve: \(4(2x - 1) - 5x + 9 = 0\)
3. Simplify: \(3(2x + 1) - 4(x - 2)\)
4. Solve: \(5x - 3(x - 4) = 8\)
5. Factor: \(2x^2 - 4x = 0\)

**Tip**: Always distribute multiplication before combining like terms in multi-term equations.

This page provides a detailed step-by-step solution to the linear equation −2(−x + 3) + 4x + 2 = 2. Learn how to apply the distributive property and combine like terms. Suitable for students in Grades 6-8.

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