Let's solve the equation \( 3(x - 4) = 2(-2x + 1) \).

### Step 1: Distribute the constants
First, distribute the \( 3 \) on the left side and the \( 2 \) on the right side:

\[
3(x - 4) = 3x - 12
\]
\[
2(-2x + 1) = -4x + 2
\]

So, the equation becomes:
\[
3x - 12 = -4x + 2
\]

### Step 2: Combine like terms
Next, add \( 4x \) to both sides of the equation to get all the \( x \) terms on one side:

\[
3x + 4x - 12 = 2
\]
\[
7x - 12 = 2
\]

### Step 3: Solve for \( x \)
Now, add \( 12 \) to both sides to isolate the term with \( x \):

\[
7x = 14
\]

Finally, divide both sides by \( 7 \):

\[
x = 2
\]

### Solution
The solution to the equation is \( x = 2 \).

Would you like more details or have any questions?

Here are some related questions:
1. What if \( x \) had been a fraction?
2. How would you solve this if the equation included a quadratic term?
3. Can this method be applied to inequalities?
4. How can we verify the solution to the equation?
5. What if the equation had more variables?

**Tip:** Always double-check your solution by substituting the value back into the original equation.

Learn how to solve the equation 3(x-4)=2(-2x+1) step-by-step with detailed explanations. This problem involves algebraic equations and the application of the distributive property. Suitable for students in Grades 7-9.

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