Let's solve the equation step by step:

The given equation is:

\[
6m - 3(m - 4) = 33
\]

### Step 1: Distribute the \(-3\) on the left-hand side
\[
6m - 3(m - 4) = 6m - 3m + 12
\]
This simplifies to:
\[
6m - 3m + 12 = 33
\]

### Step 2: Combine like terms
\[
(6m - 3m) + 12 = 33
\]
\[
3m + 12 = 33
\]

### Step 3: Subtract 12 from both sides
\[
3m = 33 - 12
\]
\[
3m = 21
\]

### Step 4: Divide both sides by 3
\[
m = \frac{21}{3}
\]
\[
m = 7
\]

Thus, the solution is \( m = 7 \).

Would you like any further details or clarifications?

Here are 5 related questions to explore:
1. How do you solve equations with variables on both sides?
2. What happens when there are fractions in the equation?
3. How do you handle equations with exponents?
4. Can you explain how to solve quadratic equations?
5. What are the steps to factor polynomials?

**Tip:** Always combine like terms before isolating the variable to simplify your work.

Learn how to solve the linear equation 6m - 3(m - 4) = 33 using distribution and simplification techniques. Follow the step-by-step breakdown of the solution, suitable for students in Grades 6-8. Explore core algebraic concepts such as distribution and combining like terms.

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