Let's solve the equation step by step.

Given equation:
\[
4x - 7 - 3x = 9 - 3x + 32
\]

### Step 1: Simplify both sides

First, let's simplify each side of the equation.

**Left side:**
\[
4x - 3x - 7 = x - 7
\]

**Right side:**
\[
9 - 3x + 32 = 41 - 3x
\]

Now, the equation is:
\[
x - 7 = 41 - 3x
\]

### Step 2: Combine like terms

To isolate \(x\), we need to get all the \(x\) terms on one side and the constants on the other.

Add \(3x\) to both sides:
\[
x + 3x - 7 = 41 - 3x + 3x
\]
\[
4x - 7 = 41
\]

### Step 3: Solve for \(x\)

Now, add 7 to both sides:
\[
4x - 7 + 7 = 41 + 7
\]
\[
4x = 48
\]

Divide both sides by 4 to solve for \(x\):
\[
x = \frac{48}{4}
\]
\[
x = 12
\]

### Solution

The solution to the equation is:
\[
x = 12
\]

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

Here are 5 related questions to further your understanding:

1. How do you solve equations with variables on both sides?
2. What happens if the variable cancels out when solving an equation?
3. How can you check if your solution to an equation is correct?
4. What is the importance of combining like terms in solving equations?
5. How do you handle equations with fractions or decimals?

**Tip:** Always double-check your solution by plugging it back into the original equation to ensure it satisfies the equation.

Learn how to solve equations step-by-step with an example problem. Understand the process of combining like terms and isolating variables to find solutions. Suitable for high school students learning algebra.

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