Let's solve the equation $3m = 5(m + 3) - 3$:

Step 1: Expand the right-hand side.

Expand $5(m + 3)$: $5(m + 3) = 5m + 15$ So, the equation becomes: $3m = 5m + 15 - 3$

Step 2: Simplify the equation.

Now simplify the right-hand side: $3m = 5m + 12$

Step 3: Move all terms involving $m$ to one side.

Subtract $5m$ from both sides: $3m - 5m = 12$ $-2m = 12$

Step 4: Solve for $m$.

Divide both sides by $-2$: $m = \frac{12}{-2} = -6$

Solution:

The solution is $m = -6$.

Would you like further details or have any questions about the steps? Here are five related questions to explore:

1. What happens if you change the constant values in the equation?
2. How would you check if your solution for $m$ is correct?
3. Can this equation be represented graphically, and what would it look like?
4. How would you solve this equation if it included fractions?
5. What if there were an additional variable, say $n$, in the equation?

Tip: When solving linear equations, always simplify both sides as much as possible before moving variables around!