1. **State the problem:** Simplify the expression $$(5a - 9b - 2c) + (c + 7b + 3a)$$ by adding the opposite and gathering like terms. 2. **Recall the rule:** When adding expressions, combine like terms by adding their coefficients. Remember to change the signs if subtracting, but here we are adding, so just combine directly. 3. **Group like terms:** - Terms with $a$: $5a$ and $3a$ - Terms with $b$: $-9b$ and $7b$ - Terms with $c$: $-2c$ and $c$ 4. **Add the coefficients:** - $a$ terms: $5a + 3a = (5 + 3)a = 8a$ - $b$ terms: $-9b + 7b = (-9 + 7)b = -2b$ - $c$ terms: $-2c + c = (-2 + 1)c = -1c = -c$ 5. **Write the simplified expression:** $$8a - 2b - c$$ This is the simplified form of the given expression.