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Inequalities Objective: To solve and graph all types of inequalities. Inequalities and Their Graphs • What inequality represents the verbal expression? • All real numbers x less than or equal to -7. • 6 less than a number k is greater than 13. Inequalities and Their Graphs • What inequality represents the verbal expression? • All real numbers x less than or equal to -7. _______|_____|_____ x 7 7 0 • 6 less than a number k is greater than 13. Inequalities and Their Graphs • What inequality represents the verbal expression? • All real numbers x less than or equal to -7. _______|_____|_____ x 7 7 0 • 6 less than a number k is greater than 13. ____|_______|_________ k 6 13 0 19 k 6 6 13 6 k 19 Inequalities and Their Graphs • Are the following a solution of 2x 1 3 ? -3 -1 Inequalities and Their Graphs • Are the following a solution of 2x 1 3 ? -3 2(3) 1 3 6 1 3 5 3 false Not a solution -1 Inequalities and Their Graphs • Are the following a solution of 2x 1 3 ? -3 2(3) 1 3 6 1 3 5 3 false Not a solution -1 2(1) 1 3 2 1 3 1 3 true Is a solution Inequalities and Their Graphs • Are the following a solution of 2x 1 3 ? -3 no 2 x 1 3 2 x 4 x 2 -1 yes Graphs • What inequality represents the graph? ______|__________|_______ 0 3 ______|__________|________ 1 0 Graphs • What inequality represents the graph? ______|__________|_______ 0 3 ______|__________|________ 1 x3 0 x 1 Homework • Page 168 • 9-37 odd Addition/Subtraction • What are the solutions of x 15 12 ? Graph. Addition/Subtraction • What are the solutions of x 15 12 ? Graph. • Add 15 to both sides. x 15 15 12 15 x3 ____|________|_____________ 0 3 Addition/Subtraction • What are the solutions of t 6 4 ? Graph. Addition/Subtraction • What are the solutions of t 6 4 • Subtract 6 from both sides. ? Graph. t 6 6 4 6 t 10 ____________|_______|______ 10 0 Class Work • Page 174 • 14-28 even Homework • Pages 174-175 • 13-27 odd • 33-41 odd Multiplication/Division • What are the solutions of x 2 3 ? Graph. Multiplication/Division • What are the solutions of • Multiply each side by 3 x 2 3 ? Graph. x 3 2 3 3 x 6 ________|__________|________ 6 0 Multiplication/Division • Everything in the last problem was the same as an equation. With an inequality, the only difference is that when you multiply or divide by a negative number you switch the inequality sign. Multiplication/Division • Everything in the last problem was the same as an equation. With an inequality, the only difference is that when you multiply or divide by a negative number you switch the inequality sign. 52 Multiplication/Division • Everything in the last problem was the same as an equation. With an inequality, the only difference is that when you multiply or divide by a negative number you switch the inequality sign. 52 5(3) 2(3) 15 6 ? no Multiplication/Division • Everything in the last problem was the same as an equation. With an inequality, the only difference is that when you multiply or divide by a negative number you switch the inequality sign. 52 5(3) 2(3) 15 6 ? yes Multiplication/Division • What are the solutions of 9 y 63 ? Graph. Multiplication/Division • What are the solutions of 9 y 63 • Divide each side by -9. • Switch the inequality sign!! 7 ? Graph. 9 y 63 9 9 y7 _______|_______|________ 0 Class Work • Page 181 • 8-18 even Homework • Page 181 • 7 -29 odd Class Work • Page 190 • 18-34 even Homework • Page 190 • 17-39 odd