What value of x makes the equation 12x + 6 – 7x = 3(4x – 5) true?
A.2
B.-3
C.3
D.-2

To solve the equation \(12x + 6 - 7x = 3(4x - 5)\), we'll first simplify both sides.

### Step-by-Step Solution:

1. **Simplify the Left Side:**
   \[
   12x + 6 - 7x = (12x - 7x) + 6 = 5x + 6
   \]

2. **Expand the Right Side:**
   \[
   3(4x - 5) = 12x - 15
   \]

3. **Set the Simplified Equation:**
   \[
   5x + 6 = 12x - 15
   \]

4. **Isolate \(x\) by moving all terms with \(x\) to one side and constants to the other:**
   \[
   5x - 12x = -15 - 6
   \]
   \[
   -7x = -21
   \]

5. **Solve for \(x\):**
   \[
   x = \frac{-21}{-7} = 3
   \]

### Conclusion:

The value of \(x\) that makes the equation true is:

\[
\boxed{C. \; 3}
\]

Would you like more details or have any questions about the solution?  

Here are some additional questions for practice:  
1. What is the value of \(x\) if \(10x + 5 - 3x = 4(2x + 1)\)?  
2. Solve for \(x\): \(8x + 2 = 3(2x + 5)\).  
3. If \(15x - 5 = 2(5x + 10)\), what is \(x\)?  
4. Determine \(x\) for \(9x + 6 - 3x = 5x + 12\).  
5. What is \(x\) when \(7x - 4 = 2x + 11\)?  

**Tip:** When solving linear equations, always combine like terms and isolate the variable on one side to solve more efficiently.

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 linear equations and simplification techniques. Suitable for students in Grades 7-9.

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