Let's solve the equation \( 3(4x - 12) = 5(x - 7) \).

### Step 1: Distribute the numbers on both sides.
On the left-hand side, distribute the 3:
\[
3(4x - 12) = 12x - 36
\]
On the right-hand side, distribute the 5:
\[
5(x - 7) = 5x - 35
\]
So now the equation is:
\[
12x - 36 = 5x - 35
\]

### Step 2: Move all terms involving \( x \) to one side.
Subtract \( 5x \) from both sides:
\[
12x - 5x - 36 = -35
\]
\[
7x - 36 = -35
\]

### Step 3: Move the constant terms to the other side.
Add 36 to both sides:
\[
7x = -35 + 36
\]
\[
7x = 1
\]

### Step 4: Solve for \( x \).
Divide both sides by 7:
\[
x = \frac{1}{7}
\]

So, the solution is \( x = \frac{1}{7} \).

Would you like more details or have any questions about this?

Here are some related questions:
1. What happens if you substitute \( x = \frac{1}{7} \) back into the original equation?
2. How do you solve equations involving fractions, such as \( \frac{3}{4}(x - 2) = 5(x + 1) \)?
3. Can you explain how to handle equations with variables on both sides in general?
4. What if the equation had decimals instead of integers?
5. How would you solve an equation with two variables, like \( 3x + 4y = 12 \)?

**Tip:** When solving equations, always start by simplifying both sides as much as possible before moving terms.

Learn how to solve the linear equation 3(4x - 12) = 5(x - 7) using distributive property and algebraic manipulation. Follow step-by-step instructions to simplify and find the solution. This problem is suitable for students in Grades 6-8, focusing on key algebra concepts.

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