B. \( (-5+7)+x \div 5 \) C. \( 7 x \div 5+(-5) \) D. \( 5 \div(-5)+7 x \) E. \( \frac{7 x-5}{5} \) F. \( 5+(-7 x \div 5) \)

Did you know that the order of operations (PEMDAS/BODMAS) is key to solving mathematical expressions like these? It tells us to handle Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). So, whether it’s resolving \( (-5+7)+x \div 5 \) or simplifying \( \frac{7 x-5}{5} \), keeping these rules straight is a must! One common mistake people make is forgetting to apply division and multiplication before addition and subtraction. For example, in \( 5+(-7 x \div 5) \), if you dive right into adding 5 and -7 without handling the multiplication and division first, your answer can go hilariously wrong! Always keep your order of operations in check to avoid math mischief!