Final answer:
The correct answer to the question is 'c. When multiplying or dividing by a negative number, the inequality sign should flip', as this is the rule that maintains the order relationship between the two sides of the inequality after the operation.
Step-by-step explanation:
When solving an inequality, it's important to understand how various operations affect the inequality sign. The given options address the rules for operations with inequalities:
- Option a suggests that the sign should flip when subtracting from both sides, which is incorrect.
- Option b proposes flipping the sign when dividing by a positive number, which is also incorrect.
- Option c is the correct rule, stating that when multiplying or dividing by a negative number, the inequality sign should flip. For example, if we have the inequality -T < 5 and we multiply both sides by -1, we would reverse the inequality to get T > -5.
- Option d is incorrect as there are circumstances, such as multiplying or dividing by a negative number, when the inequality sign should indeed flip.
Therefore, the correct answer is c. When multiplying or dividing by a negative number, the inequality sign should flip. This rule helps to maintain the order relationship between the two sides of the inequality after the operation.