1. **State the problem:** Solve the equation $$832 - n = 365$$ for the variable $$n$$. 2. **Isolate the variable:** To find $$n$$, we need to isolate it on one side of the equation. We can do this by subtracting 365 from both sides or by subtracting 832 from both sides and then multiplying by -1. 3. **Subtract 365 from both sides:** $$832 - n - 365 = 365 - 365$$ $$832 - 365 - n = 0$$ $$467 - n = 0$$ 4. **Isolate $$n$$:** $$467 - n = 0$$ Subtract 467 from both sides: $$467 - n - 467 = 0 - 467$$ $$-n = -467$$ 5. **Multiply both sides by -1 to solve for $$n$$:** $$\cancel{-1} \times -n = \cancel{-1} \times -467$$ $$n = 467$$ **Final answer:** $$n = 467$$