Let's solve the equation step by step:

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

1. Expand the right-hand side:
   \[
   3x + 2 = x + 4x + 8
   \]

   Combine like terms:
   \[
   3x + 2 = 5x + 8
   \]

2. Move all terms involving \(x\) to one side and constants to the other:
   \[
   3x - 5x = 8 - 2
   \]

   This simplifies to:
   \[
   -2x = 6
   \]

3. Divide by -2:
   \[
   x = -3
   \]

The solution is:
\[
x = -3
\]

Would you like more details on the steps or have any questions?

Here are some related questions for further practice:
1. Solve \(2x + 5 = 3(x + 1)\).
2. Solve \(4x + 3 = 2x + 7\).
3. Solve \(5x - 4 = 3(x + 2)\).
4. Solve \(x + 2 = 4(2x - 1)\).
5. Solve \(3x + 2 = 2(x + 3) + 1\).

**Tip:** When solving equations, always start by expanding and simplifying both sides as much as possible.

This webpage provides a step-by-step solution to the linear equation 3x + 2 = x + 4(x + 2). Learn how to use algebraic simplification, the distributive property, and properties of equality. Ideal for students in Grades 6-8.

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