1. Stating the problem: Solve the equation $6 + x = 3x - 12$ for $x$. 2. Write down the equation: $$6 + x = 3x - 12$$ 3. To isolate $x$, first subtract $x$ from both sides: $$6 + \cancel{x} - \cancel{x} = 3x - 12 - x$$ which simplifies to $$6 = 2x - 12$$ 4. Next, add 12 to both sides to isolate the term with $x$: $$6 + 12 = 2x - 12 + 12$$ which simplifies to $$18 = 2x$$ 5. Finally, divide both sides by 2 to solve for $x$: $$\frac{18}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ which simplifies to $$9 = x$$ 6. Therefore, the solution is: $$x = 9$$