1. **State the problem:** Solve the equation $3x + 5 - 2x = 12$ for $x$. 2. **Combine like terms:** On the left side, combine $3x$ and $-2x$. $$3x - 2x + 5 = 12$$ $$x + 5 = 12$$ 3. **Isolate the variable:** Subtract 5 from both sides to isolate $x$. $$x + \cancel{5} - \cancel{5} = 12 - 5$$ $$x = 7$$ 4. **Check the solution:** Substitute $x = 7$ back into the original equation. $$3(7) + 5 - 2(7) = 21 + 5 - 14 = 12$$ The left side equals the right side, so $x = 7$ is the correct solution.