Let's solve the equation:

### Equation:
\[
12x + 6 - 7x = 3(4x - 5)
\]

### Step 1: Expand the right-hand side.
\[
12x + 6 - 7x = 12x - 15
\]

### Step 2: Combine like terms on the left-hand side.
\[
(12x - 7x) + 6 = 5x + 6
\]
So, the equation becomes:
\[
5x + 6 = 12x - 15
\]

### Step 3: Move the terms involving \(x\) to one side and constants to the other.
\[
5x - 12x = -15 - 6
\]
\[
-7x = -21
\]

### Step 4: Solve for \(x\).
\[
x = \frac{-21}{-7} = 3
\]

### Final Answer:
\[
x = 3
\]

Would you like further details or explanations on any step?

Here are 5 related questions you might find useful:
1. What if the equation was \(12x + 6 - 7x = 3(4x + 5)\)?
2. How do you handle equations with fractions?
3. What happens if the variables are on both sides of the equation?
4. How do you check if your solution is correct?
5. Can equations have no solutions or infinitely many solutions?

**Tip:** Always double-check your final solution by substituting the value of \(x\) back into the original equation.

Learn how to solve the linear equation 12x + 6 – 7x = 3(4x – 5) with a detailed step-by-step solution. This problem covers key algebraic concepts, including the distributive property and combining like terms. Suitable for students in Grades 6-8.

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