Algebra 1 Common Core Student Edition, Grade 8-9

Think

Is th e s o lu tio n o f th e

inequality a union or

an intersection?

The solution is a

compound inequality

joined by the word and.

So the solution is an

intersection.

Writ ing Solut ions of an Inequalit y

What are the solutions of 12x - 1 1 < 3? W r i t e t h e s o l u t i o n s as e i t h e r t h e u n i o n o r

th e in te rs e c tio n o f tw o sets.

I 2jc — 1 1 < 3

-3 < 2x — 1 < 3

-2 < 2x < 4

-1 < x <2

Write a compound inequality.

Add 1 to each expression.

Divide each side by 2.

T h e s o lu t io n s o f th e in e q u a l i t y a re g iv e n b y - 1 < x < 2. Y o u c a n w r it e t h is as x > - 1

a n d x < 2. T h is c o m p o u n d i n e q u a l i t y is th e in t e r s e c t io n o f t w o sets, w h ic h y o u c a n

write as follows: {x|x> —l} D {x|x< 2}.

Go t I t? 5. S o lv e e a c h in e q u a lit y. W r it e t h e s o lu t io n s as e it h e r t h e u n i o n o r th e

in te rs e c tio n o f tw o sets.

a.8<x+5<ll b. |4x — 6| > 14

Lesso n Ch eck

Do y o u k n o w H OW?

Let X = {2 ,4, 6, 8 , 1 0 }, Y = {1, 2, 3, 4, 5, 6, 7, 8, 9 , 1 0 },

and Z = {1,3 ,5, 7,9}. F in d e a c h u n i o n o r in t e r s e c t i o n.

1. XU Y 2.XHY 3 .XHZ 4.YUZ


2. I n a s u r v e y o f 80 p e o p le w h o u s e t h e i r c e ll p h o n e s to
   take p ic tu re s a n d p la y gam es, 49 ta ke p ic tu re s a n d
   35 ta k e p ic t u r e s a n d p la y g a m e s. H o w m a n y p e o p le
   o n ly u s e t h e i r c e ll p h o n e s t o p la y g a m e s?

~ ----------- MATHEMATICAL

Do y o u UN DERSTAND? I f f l f PRACTICES

6. V o c a b u l a r y Suppose A a n d B a re n o n e m p t y sets.

Which set contains more elements: A U B or A D B?

E x p la in y o u r r e a s o n in g.

7. Compare and Contrast H o w a re u n io n s a n d
   in te rs e c tio n s o f sets d iffe re n t?
   D e t e r m i n e w h e t h e r e a c h s t a t e m e n t is true o r false.


8. If x is an elem ent o f set A a n d x is n o t an e le m e n t o f
   set B, th e n x is an elem ent o f A U B.


9. I f x is n o t a n e le m e n t o f s e t A a n d x is an e le m e n t o f
   set B, then x is an elem ent o f A fT B.

Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses

1^1 Practice

MATHEMATICAL

PRACTICES

F in d e a c h u n i o n o r in t e r s e c t i o n. L e t A = {1,3,4}, B = {x| x is a n e v e n

w h o le n u m b e r le s s t h a n 9 } , C = {2,5,7,10}, and D = {x|xisanodd

w h o le n u m b e r le s s t h a n 10 }.

10. A U B


11. BUD


12. A(1D
    11. TU C
    15. CU D


13. B<1C


14. A U D


15. ACB


16. BHD

0 See Problems 1 and 2.

13. BUC


14. AC\C


15. CHD

218 Chapter 3 Solving Inequalities