Flipping the inequality sign is a crucial step when solving inequalities. This typically occurs in two main scenarios:
- Multiplying or Dividing by a Negative Number: When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign. For example:
If we start with the inequality:
-2x < 6
When we divide both sides by -2, we must change the sign:
x > -3
- Rearranging Inequalities: If you rearrange an inequality by subtracting a term from both sides, or adding a term, you do not flip the inequality sign. The sign stays the same as long as you are not multiplying or dividing by a negative.
In summary, remember to flip the inequality sign whenever you multiply or divide by a negative number. This rule is vital for correctly solving and representing inequalities.