2. Chapter 4 Inequalities

3. 4.1 Inequalities and Their Graphs

4. An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs: ≤ 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 greater than or equal to B.

5. Ex 1: Determine whether the given number is a solution of the inequality of x >4 a.) 4 4>4 False b.) 0 0>4 False c.) -4 -4>4 False d.) 6 6>4 True

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

7. Ex 2: Graph the solution of x > -2 -2-6-40 6 42

8. Ex 3: Graph the solution of x  -2 If you have ≤ or ≥ you draw a closed circle -2-6-40 6 42

9. Hint: When graphing make sure your variable is on the left side 5 < x To make sure the graph is correct switch the variable and number and flip the inequality. x>5 Now graph it

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

11. Ex 5: This is the graph of: 1) x  1 2) x > -1 3) x  -1 4) x > 1 -2-6-40 6 42

12. 4.2 The Addition Property of Inequalities

13. Addition Property of Inequalities If a < b, then a + c < b + c The same is true for >, , and 

14. Ex 6: Solve for “x”and graph: x - 3 > 4 +3 X > 7 -4 -80 84

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

16. Ex 8: Solve:

17. Ex 9: 5(y-2)-4(y-1)<0

18. Assignment: Page 173 (4-18, 26-30) even Page 178 (8-36) even