Linear Inequalities and Systems of Inequalities

SAT Math · Axiom Academy

Solving inequalities and graphing regions An inequality is like an equation, but instead of an equals sign, you have one of these symbols: Solving Single-Variable Inequalities Solving inequalities is almost the same as solving equations, with one CRITICAL exception: When you multiply or divide BOTH sides by a negative number, FLIP the inequality sign. Example 2: Multiply by Negative (FLIP!) Graphing Inequalities on a Number Line x > 3 : Open circle at 3, arrow to the right : Closed circle at -1, arrow to the left A system of inequalities asks you to find the region that satisfies ALL inequalities at the same time. Test a point to know which side to shade Final answer is the overlapping region A compound inequality has two inequality signs, like -2 < x < 5 . This means: Test a point: Always verify which region to shade by testing a simple point like (0,0). Watch the flip rule: Multiply/divide by negative? FLIP. This is a common error source. Line type matters: Solid vs. dashed can change which points are in the solution. Read carefully: "At least" = , "more than" = > , "at most" = , "less than" = < .

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