Solving Linear Inequalities in One Variable

An inequality is like an equation, but instead of =, it uses: | Symbol | Meaning | Example | |---|---|---| | < | less than | x < 5 | | > | greater than | x > 3 | | leq | less than or equal to | x leq 7 | | geq | greater than or equal to | x geq -2 | The solution to an inequality is a range of values, not a single number. Solving works exactly like equations, with ONE crucial difference...

When you multiply or divide both sides by a negative number, you must reverse (flip) the inequality sign. [formula] Why? Because multiplying by a negative reverses the order: - 2 < 5 is true - Multiply both by -1: -2 > -5 (the sign flips!) This is the #1 most tested inequality rule on the SAT.

Example: Solve 3x + 7 > 22