A first-degree inequality is solved almost like an equation, but with one fundamental caveat: every time we multiply or divide by a negative number, we must reverse the inequality sign.
Property — Equivalence principles for inequalities
- First principle (addition): you can add or subtract the same quantity to both sides without changing the direction.
- Second principle (positive product): you can multiply or divide both sides by the same positive number without changing the direction.
- Second principle (negative product): if you multiply or divide by a negative number, the direction of the inequality is reversed.
Warning — The most frequent mistake
The “sign reversal” rule is the number one cause of errors in inequalities. Every time you perform an operation, ask yourself: am I multiplying or dividing by something negative? If so, flip the sign.
Links
Topics: Inequalities
Concepts: Sign reversal · First-degree inequality · Equivalence principle
Skills: Solving inequalities