Linedr Inequdlities Complete Formulqs 2. LINEAR INEQUALITY IN ONE VARIABLE INEQUALITIES BASIC SYMBOLS General form: Greater than: ax + b > 0 Less thon: ax + b < 0 Greater than or equal toः > b > 0 ax Less than or equal to: < b<0 X 3. RULES FOR SOLVING INEQUALITIES 4. SOLUTION SET Adding or subtracting the same number on both The solution of an inequality is] the set of dll volues of the sides does not change the inequality sign. variable that satisfy it Multiplying or dividing both sides by a positive Inequdlity sign remdins the sume number Multiplying or dividing both sides by a negative Inequality sign is reversed number >2 6. LINEAR INEQUALITIES IN 5. GRAPHICAL REPRESENTATION ON NUMBER LINE TWO VARIABLES Open circle (o) for or General form: Closed circle for < or > by < c 5 X by > c shows direction of solution ax Arrow by < c X by > c aX SOLUTION OF LINEAR INEQUALITY IN 8. GRAPHICAL RULES TWO VARIABLES Dotted line for < or Steps: Solid line for < or 2 Replace inequality with equality: ax by = @ Shaded region represents solution set Draw the boundary line Choose a test point (usually origin) Check which region satisfies the inequality Shade the required region | 10. IMPORTANT POINTS 9. SYSTEM OF LINEAR INEQUALITIES Inequalities have infinitely many solutions The common shaded region satisfying all Graphical method is compulsory for two] inequdlities is the solution variables Boundary line may or may not be included) Linedr Inequdlities Complete Formulqs 2. LINEAR INEQUALITY IN ONE VARIABLE INEQUALITIES BASIC SYMBOLS General form: Greater than: ax + b > 0 Less thon: ax + b < 0 Greater than or equal toः > b > 0 ax Less than or equal to: < b<0 X 3. RULES FOR SOLVING INEQUALITIES 4. SOLUTION SET Adding or subtracting the same number on both The solution of an inequality is] the set of dll volues of the sides does not change the inequality sign. variable that satisfy it Multiplying or dividing both sides by a positive Inequdlity sign remdins the sume number Multiplying or dividing both sides by a negative Inequality sign is reversed number >2 6. LINEAR INEQUALITIES IN 5. GRAPHICAL REPRESENTATION ON NUMBER LINE TWO VARIABLES Open circle (o) for or General form: Closed circle for < or > by < c 5 X by > c shows direction of solution ax Arrow by < c X by > c aX SOLUTION OF LINEAR INEQUALITY IN 8. GRAPHICAL RULES TWO VARIABLES Dotted line for < or Steps: Solid line for < or 2 Replace inequality with equality: ax by = @ Shaded region represents solution set Draw the boundary line Choose a test point (usually origin) Check which region satisfies the inequality Shade the required region | 10. IMPORTANT POINTS 9. SYSTEM OF LINEAR INEQUALITIES Inequalities have infinitely many solutions The common shaded region satisfying all Graphical method is compulsory for two] inequdlities is the solution variables Boundary line may or may not be included)