What value of *x* makes the equation 12*x* + 6 – 7*x* = 3(4*x* – 5) true?

A.2

B.-2

C.3

D.-3


To solve the equation \(12x + 6 - 7x = 3(4x - 5)\) for \(x\), follow these steps:

### Step 1: Simplify both sides of the equation
First, combine like terms on the left-hand side:

\[
12x - 7x + 6 = 5x + 6
\]

Now, distribute the 3 on the right-hand side:

\[
3(4x - 5) = 12x - 15
\]

So, the equation becomes:

\[
5x + 6 = 12x - 15
\]

### Step 2: Move all terms involving \(x\) to one side and constants to the other
Subtract \(5x\) from both sides to get:

\[
6 = 7x - 15
\]

Next, add 15 to both sides:

\[
21 = 7x
\]

### Step 3: Solve for \(x\)
Divide both sides by 7:

\[
x = 3
\]

### Conclusion:
The value of \(x\) that makes the equation true is \(x = 3\). Therefore, the correct answer is **C. 3**.

Do you have any questions or need further details?

### Further Questions to Explore:
1. What is the effect of distributing a constant across a binomial in an equation?
2. How would you solve an equation if it involved fractions instead of integers?
3. What happens if you substitute the incorrect value for \(x\) in this equation?
4. Can the same process be used to solve equations involving more complex polynomials?
5. How do you verify your solution after solving an algebraic equation?

**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 12x + 6 - 7x = 3(4x - 5) with a detailed step-by-step solution. This problem involves algebraic equations and the distributive property. Suitable for students in Grades 9-12.

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