1. Inequalities Inequalities Objectives: To determine whether a number is a solution of an inequality To graph inequalities on the number line To write inequalities

2. Inequalities An inequality is a mathematical sentence containing >,, <.

3. Inequalities Words - is less than - is greater than -is less than or equal to - is at most -is greater than or equal to -is at least Symbols <><>

4. Inequalities Any number that makes an inequality true is a solution of the inequality. Inequalities have many solutions. Example: x > 4 List 4 possible solutions. 4.5, 5, 7, 12.5

5. Open vs Closed Circle If an inequality is less than/greater than we use an open circle on the number line to show that the value is not included in the solution. If an inequality is less than or equal to/greater than or equal to we use a closed circle to show that the value IS included in the solution.

6. Example 2 The solutions are shown by shading a number line. Example: x > 4 34567

7. Example 1 Determine whether each number is a solution of a) 3 b) -2 c) 9 d) 7 yes, because 3 is less than 7 yes, because -2 is less than 7 no, because 9 is not less than or equal to 7 yes, because 7 is equal to 7

8. 1) Graph m > 3 on a number line. 12345

9. 2) Graph k < -2 on a number line. -3-201

10. 3) Graph h > 3 on a number line. 012 34

11. 4) Graph k < -2 on a number line. -3-201

12. Solving One-Step Inequalities by Adding or Subtracting 1) x + 4 > 8 - 4 - 4 x > 4

13. Check x + 4 > 8 Solution: x > 4 Substitute a value that is greater than 4 for x. 5 + 4 > 8 9 > 8  This is a true statement.

14. Graph x > 4 12345

15. Solving One-Step Inequalities by Adding or Subtracting 2) c - 3 < 2 + 3 + 3 c < 5

16. Check c – 3 < 2 Solution: c < 5 Substitute a value that is less than or equal to 5 for c. 5 – 3 < 2 2 < 2  This is a true statement.

17. 23456 Graph c < 5 on a number line.

18. Solving One-Step Inequalities by Adding or Subtracting 3) d - 4 < -2 + 4 + 4 d < 2

19. Check d – 4 < -2 Solution: d < 2 Substitute a value that is less than 2 for d. 1 – 4 < -2 -3 < -2  This is a true statement.

20. Graph d < -2. -5 -4-3-2

21. Solving One-Step Inequalities by Adding or Subtracting 4) a - 2 > 6 + 2 + 2 a > 8

22. Check a - 2 > 6 Solution: a > 8 Substitute a value that is greater than or equal to 8 for a. 8 - 2 > 6 6 > 6  This is a true statement.

23. Graph a > 8. 5678 9

24. Solving One-Step Inequalities by Adding or Subtracting 5) p - 7 > 0 + 7 + 7 p > 7

25. Check p - 7 > 0 Solution: p > 7 Substitute a value that is greater than 7 for p. 8 - 7 > 0 1 > 0  This is a true statement.

26. Graph p > 7 45678

27. Solving One-Step Inequalities by Adding or Subtracting 6) j + 5 < 2 - 5 - 5 j < -3

28. Check j + 5 < 2 Solution: j < -3 Substitute a value that is less than or equal to -3 for c. -3 + 5 < 2 2 < 2  This is a true statement.

29. -5-4-3-2 Graph j < -3 on a number line.

30. Review