2. How do you read . . . a < b a is less than b a > b a is greater than b

3. Inequality The open sentence x < -2 is an example of an inequality An inequality contains at least one variable and consists of 2 expressions with an inequality symbol such as <, >, or ≠ between them.

4. Solving an Inequality To solve an inequality means to find a solution set. What is the solution set of x < -2? On a number line: open circle means not including this point

5. Solving an Inequality How would we graph the solution of x > 1?

6. Solving an Inequality The Addition and Subtraction Properties of Equality allow you to add or subtract the same number from each side of an equation to obtain an equivalent equation. x – 4 = 3 x + 2 = 5 Do inequalities work the same way?

7. Solving an Inequality 2 < 6 +5 +5 7 < 11 TRUE

8. Solving an Inequality 2 < 6 -1 -1 1 < 5 TRUE

9. Equivalent Inequalities Open inequalities with the same solution set are called equivalent inequalities.

10. Addition Property of Inequality For all real numbers a, b, and c, if a < b, then a + c < b + c, and if a > b, then a + c > b + c In other words, adding the same number to each side of an equality produces an equivalent equality.

11. Subtraction Property of Inequality For all real numbers a, b, and c, if a < b, then a - c < b - c, and if a > b, then a - c > b - c In other words, subtracting the same number from each side of an equality produces an equivalent equality.

12. Solve x – 8 > -11 & Graph

13. Solve & Graph 7 < 5 – (½ – x)

14. After Mary paid $8.36 for a snack she had less than $2.50 left. How much money did she have originally?

15. After Bill paid $7.21 at the movies, he had less than $1.75 left. How much money did he have originally?

17. Solving an Inequality The Multiplication and Division Properties of Equality allow you to add or subtract the same number from each side of an equation to obtain an equivalent equation. x / 4 = 2 x * 3 = 21 Do inequalities work the same way?

18. Solving an Inequality 3 < 4 *5 *5 15 < 20 TRUE

19. Solving an Inequality -4 > -20 /2 /2 -2 > -10 TRUE

20. Solving an Inequality -5 < -3 *-1 *-1 5 < 3 FALSE

21. Solving an Inequality 18 > -6 /-3 /-3 -6 > 2 FALSE

22. Notice: Multiplying or Dividing each side of a true equality by a negative number produces a false inequality

23. Multiplication Property of Inequality, Part 1 For all real numbers a, b, and c, if a < b and c > 0, then ac < bc, and if a > b and c > 0, then ac > bc That is, multiplying each side of an inequality by the same positive number produces an equivalent inequality.

24. Multiplication Property of Inequality, Part 2 For all real numbers a, b, and c, if a < b and c < 0, then ac > bc, and if a > b and c < 0, then ac < bc That is, multiplying each side of an inequality by the same negative number and reversing the order of the inequality produces an equivalent inequality.

25. Division Property of Inequality, Part 1 For all real numbers a, b, and c, if a < b and c > 0, then a/c < b/c, and if a > b and c > 0, then a/c > b/c That is, dividing each side of an inequality by the same positive number produces an equivalent inequality.

26. Division Property of Inequality, Part 2 For all real numbers a, b, and c, if a < b and c < 0, then ac > b/c, and if a > b and c < 0, then ac < b/c That is, dividing each side of an inequality by the same negative number and reversing the order of the inequality produces an equivalent inequality.

27. Solve: 7x < -56 Divide each side by 7 x < -8 Graph:

28. Solve: -⅔ x > 16 Multiply each side by the reciprocal of -⅔ Because we multiplied by a negative, change the > to a < x < -24 Graph:

29. Solve: -4 < - 2x

30. If Jill sells more than $100 worth of peanut brittle, she will win a radio. Each box of peanut brittle sells for $2.75. How many boxes must she sell to win the radio? 2.75p > 100 p > 100/2.75 p > 36.3636 Can she sell 36.36 boxes? Jill must sell 37 boxes.

31. -3x + 6 < -5

32. 5 – 4x < 2x - 7

33. -3/2 x + 4 > 7

34. -2(2x + 1) + 5x < x + 5

35. Turn to p. 168 Do 1 -14 Turn to p. 169 Do 16-19 Turn to p. 173 Do 1-9 Turn to p. 174 Do 27-30