1. **State the problem:** Simplify the expression $3 + 5 - (-3) \times 2 - (-7) + 2 \times (-2) \times 4$. 2. **Recall the rules:** - Subtracting a negative number is the same as adding the positive. - Multiplication has higher precedence than addition and subtraction. - Multiply before adding or subtracting. 3. **Calculate each multiplication:** - $-(-3) \times 2 = +3 \times 2 = 6$ - $2 \times (-2) \times 4 = 2 \times (-2) = -4$, then $-4 \times 4 = -16$ 4. **Rewrite the expression with these values:** $$3 + 5 + 6 - (-7) - 16$$ 5. **Simplify the subtraction of a negative:** $$3 + 5 + 6 + 7 - 16$$ 6. **Add and subtract from left to right:** - $3 + 5 = 8$ - $8 + 6 = 14$ - $14 + 7 = 21$ - $21 - 16 = 5$ **Final answer:** $5$