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.