Lesso n Ch eck
Do y o u k n o w H OW?- W hat com pound inequality represents th e p hrase "all
real n um b ers th at are greater th a n or equal to 0 an d
less th an 8”? G raph the solutions. - W hat are th e solutions of-4<r-5<-l? Graph
the solutions. - Your test scores in science are 83 an d 87. W hat
possible scores can you earn on your next test to have
a test average b etw een 85 an d 90, inclusive? - Write the interval represented on the n u m b e r line
below as an inequality an d in interval notation.
I 1— I-------- 1 --- 1 ------ 1 --1— • -----1—►
- 8 - 6 - 4 - 2 0 2 4 6 8
/ { 5 V MATHEMATICAL
Do y o u UN DERSTAN D? {Q / PRACTICES- Vo cab ular y W hich of the following are com p o u n d
inequalities?
A. x > 4 orx< -4 B. x>6
C. 8 ^ 5x < 30 D. 7x > 42 or —5x ^ 10
^^ 6. Er r o r A n a l y s i s A stu d en t w rites the inequality
x ^ 17 in interval n o tatio n as [17, °°]. Explain why
this is incorrect.- Reasoning W hat are th e solutions of 3x - 7 ^ 14 or
4x - 8 > 20? W rite your solutions as a co m p o u n d
inequality an d in interval notation. - W r i t i n g C om pare the graph of a co m p o u n d
inequality involving and w ith the graph of a
compound inequality involving or.
Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses ((87 p r a c t i c e s
Pr act i ce Write a compound inequality that represents each phrase. Graph the solutions. Se e Pr o b l em 1.- all real n u m b ers th a t are b etw een -5 an d 7
- The circum ference of a w o m en ’s basketball m u st be b etw een 28.5 in. and
29 in., inclusive.
Solve each compound inequality. Graph your solutions. ^ Se e Pr o b l em s 2 an d 3.
- 4 < f c + 3<8 12.5<y+2<ll 13.3<4p-5<l5
- 15 < 31 + k < 19 16. —3 < — 3
Solve each compound inequality. Graph your solutions. jp Se e Pr o b l em 4.
- 6b — 1 < — 7 or 2b + 1 > 5 18. 5 + m > 4 or 7m < —35
- 4d + 5 s 13 or 7d — 2 < 12 20. 7 — c < 1 or 4c ^ 12
- 5y + 7 ^ —3 or 3y —2 > 13 22. 5z — 3 > 7 or 4z — 6 < —10
Write each interval as an inequality. Then graph the solutions. ^ See Problem 5.- (-oo,2] 24. [-4,5] 25. — 1] or (3, °°) 26. [6,oo)
204 Chapter 3 So l v i n g I n e q u a l i t i e s