Let's solve the equation \( x + 4(x - 2) = 12 \):

### Step 1: Expand the expression
First, distribute the 4 through the parentheses:
\[
x + 4(x - 2) = x + 4x - 8
\]
Now the equation becomes:
\[
x + 4x - 8 = 12
\]

### Step 2: Combine like terms
Combine the \( x \) and \( 4x \):
\[
5x - 8 = 12
\]

### Step 3: Solve for \( x \)
Add 8 to both sides of the equation:
\[
5x = 12 + 8
\]
\[
5x = 20
\]

Now, divide both sides by 5:
\[
x = \frac{20}{5} = 4
\]

Thus, the solution is:
\[
x = 4
\]

Would you like further details or have any questions?

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Here are some related questions you might find interesting:

1. What happens if the equation had been \( x - 4(x - 2) = 12 \)?
2. How do you solve an equation with a variable on both sides, such as \( 3x + 5 = 2x + 10 \)?
3. Can this method be used to solve quadratic equations?
4. What are the steps for solving equations with fractions like \( \frac{x}{2} + 3 = 7 \)?
5. How would you solve the equation \( 5(x + 3) - 4(x - 1) = 15 \)?

**Tip:** Always remember to simplify expressions step-by-step to avoid mistakes when solving equations.

Discover how to solve the linear equation x + 4(x - 2) = 12 with a clear step-by-step solution. This example focuses on algebraic concepts such as the distributive property and combining like terms, making it suitable for students in Grades 6-8.

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