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

Let's solve the equation step by step to find the value of \( x \).

Given equation:

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

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

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

\[
5x + 6 = 3(4x - 5)
\]

Next, distribute the 3 on the right side:

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

### Step 2: Get all \( x \) terms on one side and constant terms on the other side.
Subtract \( 5x \) from both sides:

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

Simplify:

\[
6 = 7x - 15
\]

Now, add 15 to both sides:

\[
6 + 15 = 7x
\]

\[
21 = 7x
\]

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

\[
x = \frac{21}{7}
\]

\[
x = 3
\]

So, the value of \( x \) that makes the equation true is \( \boxed{3} \).

Would you like more details, or do you have any other questions?

### Relative Questions:
1. What is the process of simplifying equations with variables on both sides?
2. How do you distribute numbers across parentheses in equations?
3. What happens if an equation has no solution or infinite solutions?
4. Can we solve the equation if it involves fractions? How?
5. How do you check if the solution to an equation is correct?

### Tip:
When solving linear equations, always start by simplifying each side of the equation separately before moving terms to one side.

Learn how to solve the equation 12x + 6 - 7x = 3(4x - 5) with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations with variables, and the distributive property. Suitable for students in Grades 7-9.

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