2. Chapter 4 Inequalities < Less Than > Greater Than

3. 4.1 Inequalities and Their Graphs 4.2 Addition Property of Inequalities To determine if a number is a solution of an inequality To graph inequalities on the number line To solve an inequality by adding a number to both sides

4. An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs: A solution of an inequality is any value that makes the inequality true. The set of all solutions of an inequality is its solution set. ≤ A ≤ B A is less than or equal to B. < A < BA < B A is less than B. > A > B A is greater than B. ≠ A ≠ B A is not equal to B. ≥ A ≥ B A is greater than or equal to B.

5. Inequalities vs. Equations Solutions InequalityEquation x + 5  9 x + 5 = 9 x = 4 x = 5 x = 6 x  4

6. x < 3 Is 2 a solution? Thumb up if yes Thumb down if not a solution

7. x < 3 Is 0 a solution? Thumb up if yes Thumb down if not a solution

8. x < 3 Is -5 a solution? Thumb up if yes Thumb down if not a solution

9. x < 3 Is 3 a solution? Thumb up if yes Thumb down if not a solution

10. Graph the solution of x + 3 = 7 -2-6-40 6 42

11. Graph the solution of x < 3 -2-6-40 6 42 2.999 -2-6-40 6 42

12. 3. Draw your solution graph line in the same direction as the inequality IF the “x” is on left. Graph the solution of x < -1 1. Draw number line. Label zero and the number where your arrow starts 0 2. Put a circle on the number. Open if. Solid if “or equal to” ≤or≥.

13. Graph the solution of x > -2 -2-6-40 6 42

14. Graph the solution of x  -2 If you have ≤ or ≥ you draw a closed circle -2-6-40 6 42

15. Hint: When graphing make sure your variable is on the left side 5 < x We would read this as 5 is less than x How would we graph it? To make sure the graph is correct switc the variable and number and flip the inequality. x>5 x is greater than 5 Now graph it

16. This is the graph of: 1) x  -2 2) x > -2 3) x  -2 4) x < -2 -2-6-40 6 42

17. This is the graph of: 1) x  1 2) x > -1 3) x  -1 4) x > 1 -2-6-40 6 42

18. Write the inequality shown in this graph -2-6-40 6 42

19. Write the inequality shown in this graph -2-6-40 6 42

20. Addition Property of Inequalities If a < b, then a + c < b + c “If I add the same number to both sides of an inequality, I get another TRUE inequality in the same direction.” The same is true for >, , and 

21. Solve for “x”and graph: x - 3 > 4 +3 X > 7 -4 -80 84

22. Solve for “x” and graph: 8z + 6 – 7z  16 Z + 6  16 -6 z  10 -4 -80 84 -6

23. Checking: Since there can be an infinite number of solutions to an inequality, it is not possible to check all the solutions. You can check the endpoint and the direction of the inequality symbol. The solutions of x + 9 < 15 are given by x < 6.

24. Assignment: -Workbook Page 18 (1-20) all -Test Sheets Signed -Test Corrections