6­4 Compound Inequalities Day 1.notebook
January 18, 2017
1/18/17 Honors Algebra Warm­up
Solve 13 ­ 8(x + 1) < 14 ­ 2(4x + 3). Then graph 13 ­ 8(x + 1) < 14 ­ 2
(4x + 3) in y= in your calculator. (The < is under Test) Jan 23­8:19 AM
Where have you encountered the word "compound" and what does it mean? 6­4 Solving Compound Inequalities
Compound Inequality: two or more inequalities joined by the words and or or
1. Greater than 8 and less than 13. 2. Greater than or equal to 8 and less than or equal to 13. 3. Less than 5 or greater than 15. Jan 23­8:19 AM
6­4 Compound Inequalities Day 1.notebook
AND
• Must satisfy both inequalities.
• The graph is the intersection, ∩, of two inequalities.
Ex 1: Graph the solution set of y ≥ 5 and y < 12
Jan 23­5:14 PM
Ex 2: Solve 7 < q + 2 ≤ 11. Graph its solution.
Jan 23­5:30 PM
January 18, 2017
6­4 Compound Inequalities Day 1.notebook
January 18, 2017
OR
• Must satisfy at least one inequality.
• The graph is the union, ∪, of two inequalities.
Ex 3: A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night, and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort.
Jan 23­5:32 PM
Ex 4: Solve and graph. (Symbol in same direction)
a. 4k – 7 ≤ 25 or 12 – 9 k ≥ 30
b. r > 5 and r ≥ 9
`
Jan 23­6:04 PM
6­4 Compound Inequalities Day 1.notebook
January 18, 2017
HW: pgs. 311­312 #20­23, 26­31, 34­38, 40
For #20­23, let n = the number
20.
1/8n ­ 5 ≥ 30; The number is at least 280.
21. 2/3n + 8 > 12; The number is greater than 6.
22. ­4n + 9 ≤ n ­ 21; The number is at least 6.
23. 10 ≤ 4(2n + 3); The number is at least ­1/4. 26.
h > 5
27.
a ≤ 11
28.
No Solution
29. All real numbers
30. t ≥ ­1
31.
a ≥ ­9
34.
(91 + 95 + 88 + s)/4 ≥ 92
35.
at least 94
36.
Yes a solution to the inequality; not a reasonable solution to the problem since Carmen cannot score over 100.
37.
1.15(7.50 + 1.25t) ≤ 13; t ≤ 3.04; Nich can order at most 3 toppings. [Another way: 0.15(7.50 + 1.25t) + (7.50 + 1.25t)≤ 13]
38.
5(F­32)/9 < ­38; F < ­36.4; mercury is a solid when the temperature is less than ­36.4oF. 40. {1,3}; {3,5}; {5,7}; {7,9}
Jan 13­3:08 PM