3-7 Absolute Value Equations and Inequalities
Quick Review
S o lv in g a n e q u a t io n o r i n e q u a lit y t h a t c o n t a in s a n a b s o lu te
v a lu e e x p r e s s io n is s im ila r t o s o lv in g o t h e r e q u a t io n s
a n d in e q u a lit ie s. Y o u w i l l n e e d t o w r it e t w o e q u a tio n s o r
in e q u a litie s u sin g p o s itive a n d negative values. T hen solve
the equations.Ex a m p l e
What is the solution of |x| - 7 = 3?|x| - 7 = 3
| jc| = 10 Add 7 to each side,
x = 10 o r x = - 1 0 D efinition o f absolute valueEx e r c i se s
Solve each equation or inequality. If there is no solution,
write no solution.- \y-= 3 50.\n + 2 := 4
51. 4 +|r+ 2 | = 7 52.|x + 3 j == - 2
53.| 5jc|< 15 54.|3rf+5|< -2
55.|2x ■
1 TV 1 r-HAO- 4 \k+ 5| > 8
- Manufacturing The ideal length o f a certain nail is
2 0 m m. T h e a c t u a l le n g t h c a n v a r y f r o m th e id e a l b y
a t m o s t 0 .4 m m. F in d th e r a n g e o f a c c e p ta b le le n g th s
of the nail.
3-8 Unions and Intersections of Sets
Quick Review
The union o f t w o o r m o r e se ts is th e s e t t h a t c o n t a in s a ll
elements of the sets. The in tersection of two or more sets is
th e set o f elem ents th a t are c o m m o n to a ll th e sets. Disjoint
sets have no elem ents in com m on.Ex a m p l e
Student Activities O f 100 s tu d e n ts w h o p la y s p o r ts o r ta k e
m u s ic le s s o n s , 7 0 s tu d e n ts p la y a s p o r t a n d 5 0 s tu d e n ts p la y
a s p o r t a n d ta k e m u s ic le s s o n s. H o w m a n y s tu d e n ts only
ta k e m u s ic le s s o n s?Sports Music lessonsEx e r c i s e s- Given A= {l, 2,3,4, 5, 6, 7,8, 9} and
B = {2 , 4, 6, 8}, w hat is A U B? - Let P = {l, 5, 7, 9,13},R = {l,2 ,3, 4, 5, 6 , 8 } , and
Q= { 1 , 3, 5 }. D r a w a V e n n d ia g r a m t h a t re p r e s e n ts
t h e in t e r s e c t io n a n d u n i o n o f th e sets. - Let N = {x | x is a m ultiple of 2} and P = { x ] x is a
multiple of 6}. Describe the intersection of N a n d P. - Cats There are 15 cats. Ten are striped and 7 are
striped and have green eyes. The rest of the cats have
g r e e n e ye s b u t a re n o t s t r ip e d. H o w m a n y c a ts h a v e
g r e e n e y e s b u t a re n o t s tr ip e d?
Both sports and music lessonsSo, 30 s tu d e n ts ta k e o n ly m u s ic le s s o n s.226 Chapter 3 Chapter Review