📚 Key Concepts
Inequalities and their propertiesLinear inequalities in one variableGraphical representationSolution setsInterval notationAlgebraic solution methodsReal-life applicationsFeasible region concept
🎯 Key Formulas
Basic Properties:- If a < b and c < d, then a + c < b + d
- If a < b and c > 0, then ac < bc
- If a < b and c < 0, then ac > bc
Solution representation:- (a,b) for open interval
- [a,b] for closed interval
- (-∞,a) or (b,∞) for infinite intervals
⚠️ Common Mistakes to Avoid
Wrong sign when multiplying/dividing by negative numbersIncorrect interval notationForgetting boundary pointsWrong graphical representationMisinterpreting "and/or" conditionsErrors in identifying solution sets
📖 Knowledge Prerequisites
Real number lineBasic algebraLinear equationsNumber line plottingUnderstanding of infinity
💡 Tips for Students
Check solution by substituting pointsAlways test points in different intervalsDraw number line for visualizationRemember sign change rulesVerify solutions graphically
👉 Practice Recommedations
Solve basic inequalitiesPractice interval notationGraph inequalitiesCombine multiple inequalitiesWork on word problemsVerify solutions algebraicallyApply in practical scenarios
Practice each question with a timer and get instant feedback
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