Final answer:
The inequalities -3x < 21 and 3x < -21 differ in their operation and solution sets: dividing the first by a negative number flips the inequality sign, yielding x > -7, while dividing the second by a positive number keeps the inequality direction, resulting in x < -7.
Step-by-step explanation:
The inequality -3x < 21 is different than 3x < -21 because they involve different arithmetic operations and result in different solution sets for x. To solve -3x < 21, you would divide both sides by -3, which reverses the inequality sign, resulting in x > -7. However, to solve 3x < -21, you'd divide both sides by 3, maintaining the direction of the inequality, to get x < -7.
When evaluating these inequalities, it's crucial to remember the rules for multiplication and division with negatives. For example, when you multiply or divide both sides of an inequality by a negative number, the inequality sign flips. Conversely, when you multiply or divide by a positive number, the inequality sign remains the same.