To solve the equation \( 3(x - 4) = 2(-2x + 1) \), follow these steps:

1. **Distribute** on both sides of the equation:
   \[
   3x - 12 = -4x + 2
   \]

2. **Add** \(4x\) to both sides to get all the \(x\) terms on one side:
   \[
   3x + 4x - 12 = 2
   \]
   \[
   7x - 12 = 2
   \]

3. **Add** 12 to both sides to isolate the \(x\) term:
   \[
   7x = 14
   \]

4. **Divide** both sides by 7 to solve for \(x\):
   \[
   x = 2
   \]

So, the solution is \( x = 2 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What if the equation had different coefficients, like \( 4(x - 3) = 5(-2x + 7) \)?
2. How do you solve equations with variables on both sides?
3. How does distributing affect the equation, and why is it important?
4. What are some common mistakes to avoid when solving equations like this?
5. How can we verify that \(x = 2\) is the correct solution?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation 3(x - 4) = 2(-2x + 1) with a detailed step-by-step solution. This problem covers algebraic concepts including equations and the distributive property. Suitable for students in Grades 7-9.

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