1. The problem is to evaluate the expression: $4 \times 7 - 3 \times \left(8 \times 1 \div 2 + 5\right) + 10$. 2. Use the order of operations (PEMDAS/BODMAS): Parentheses first, then multiplication and division from left to right, and finally addition and subtraction. 3. Calculate inside the parentheses: $8 \times 1 = 8$. 4. Then divide by 2: $8 \div 2 = 4$. 5. Add 5: $4 + 5 = 9$. 6. Multiply by 3: $3 \times 9 = 27$. 7. Calculate $4 \times 7 = 28$. 8. Now substitute back: $28 - 27 + 10$. 9. Perform subtraction and addition from left to right: $28 - 27 = 1$, then $1 + 10 = 11$. 10. The final answer is $11$.