6.4 Solving Compound Inequalities A compound inequality has more than one part, contains an “and” or an “or” in the statement. Inequalities containing “and”: True if and only if both inequalities are true. This is called the intersection. Graph the solution set of x > 5 and x < 10. Graph them on the same number line. 5 10 6 4 11 9 Graph x > 5 first in one color. Graph x < 10 second in another color. Where they overlap is the answer. Remember the answer does not include 5 or 10.

Another form of an “and” statement. (sandwich) 6 < x + 5 < 15 Break into 2 equations. 6 < x + 5 and x + 5 < 15 -5 -5 -5 -5 1 < x and x < 10 Graph Try this one. Graph the solution set of y > 5 and y < 12 The answer DOES include the 5 but not the 12. 5 12 6 4 11 13 Solution {x|1 < x < 10} 1 2 10 9 11

Try These Four p. 317 #1, #2, #3, & #6

Inequalities containing “or” These are called unions. x > 5 or x < 1 Graph both on the same line. Answer is anything that is shaded. 4k – 7 < 25 or 12 – 9k > 30 +7 +7 -12 -12 4k < 32 -9k > 18 k < 8 k < -2 Graph on the same line. Since the answer is anything shaded, you really only need k < 8. 1 2 5 6 -2 -1 8 7 9 4

Try These Two p. 317 #4 & #5

Homework #42 p. 318 9-23 odd, 26-31, 33, 38, 51-53