Solving and Graphing Inequalities By David Bailey

What are Inequalities? Inequalities express the relative order of two mathematical expressions. Expressions can be numerical or variable.

Recall Symbols a < b a is less than b a > b a is greater than b Introduce new symbols a can be equal to b. a b a is less than/equal to b a b a is greater than/equal to b

Addition Property of Inequalities The same constant or variable can be added to each side of an inequality without changing the solution set of the inequality. (Recall: Addition Property of Equations)

If a < b, then a + c < b + c If a > b, then a + c > b + c

And If a b, then a + c b + c

Look my students, you shall see, how to Graph Inequalities! a < X ( a X < a ) a X a [ a a X ] a

Multiplication Property of Inequalities involving positive numbers Both sides an inequality can be multiplied by the same non-negative number without changing the inequality. e.g. If a < b then ac < bc Or, If a > b then ac > bc

If the inequality sign is reversed, both sides of an inequality can be multiplied by the same negative number. e.g. If a < b then –ca > -cb or If a > b then –ca < -cb Multiplication Property of Inequalities involving negative numbers

Comparative Shopping A sub-compact car can be rented from the Burnette Rental Company for $180 per week with unlimited mileage. The same model can be rented from the Faulkner Rental company for $100 per week plus 20 cents per mile. How many miles must be driven in a Faulkner Rental before it is economically feasible to rent from the Burnette Rental Company?