1. **State the problem:** We need to evaluate each algebraic expression for the given variable values in Option A and Option B. 2. **Expressions:** - Expression 1: $-112 - 8(3x + 2)$ - Expression 2: $4(2 - 3n) - 5n + 36$ - Expression 3: $-v + 2(v - 8) - 2(v + 3) + 4v$ 3. **Evaluate Expression 1 for Option A ($x=4$):** $$-112 - 8(3 \times 4 + 2) = -112 - 8(12 + 2) = -112 - 8 \times 14 = -112 - 112 = -224$$ 4. **Evaluate Expression 2 for Option A ($n=-13$):** $$4(2 - 3 \times (-13)) - 5 \times (-13) + 36 = 4(2 + 39) + 65 + 36 = 4 \times 41 + 65 + 36 = 164 + 65 + 36 = 265$$ 5. **Evaluate Expression 3 for Option A ($v=-10$):** $$-(-10) + 2(-10 - 8) - 2(-10 + 3) + 4(-10) = 10 + 2(-18) - 2(-7) - 40 = 10 - 36 + 14 - 40 = (10 - 36) + (14 - 40) = -26 - 26 = -52$$ 6. **Evaluate Expression 1 for Option B ($x=7$):** $$-112 - 8(3 \times 7 + 2) = -112 - 8(21 + 2) = -112 - 8 \times 23 = -112 - 184 = -296$$ 7. **Evaluate Expression 2 for Option B ($n=-4$):** $$4(2 - 3 \times (-4)) - 5 \times (-4) + 36 = 4(2 + 12) + 20 + 36 = 4 \times 14 + 20 + 36 = 56 + 20 + 36 = 112$$ 8. **Evaluate Expression 3 for Option B ($v=11$):** $$-11 + 2(11 - 8) - 2(11 + 3) + 4 \times 11 = -11 + 2 \times 3 - 2 \times 14 + 44 = -11 + 6 - 28 + 44 = (-11 + 6) + (-28 + 44) = -5 + 16 = 11$$ **Final answers:** - Option A: Expression 1 = $-224$, Expression 2 = $265$, Expression 3 = $-52$ - Option B: Expression 1 = $-296$, Expression 2 = $112$, Expression 3 = $11$