Simplify each expression. Justify each step.- 8 + (9 f+ 4 ) 21. 9(2x) 22. (4 + I0 5 x ) + 5 23.
- (1 2 • r ) • 13 25. (2 + 3 x) + 9 26. 4 • [x • 6.3) 27.
56 ab 1 .5mn 13 p
m 3 U. pq 31.
Use deductive reasoning to tell whether each statement is true or false.
If it is false, give a counterexample. If true, use properties of real numbers to
show the expressions are equivalent.- For all real numbers r, s, and t, (r • s) • t = t • (s • r).
- For all real numbers p a n d q, p + q = q -r- p.
- For all real numbers x, x + 0 = 0.
- F o r a ll r e a l n u m b e r s a a n d b, - a • b = a • ( - b ).
@ 3 6. E rro r A nalysis Y o u r f r i e n d s h o w s y o u th e p r o b le m a t t h e
r ig h t. H e says t h a t th e A s s o c ia tiv e P r o p e r t y a llo w s y o u to
c h a n g e t h e o r d e r i n w h ic h y o u c o m p le t e t w o o p e r a t io n s. Is
y o u r f r i e n d c o r r e c t? E x p la in.
- Travel I t is 2 5 8 m i f r o m T u ls a , O k la h o m a , t o D a lla s , T e xa s. I t is
239 m i fro m D allas, Texas, to H ouston, Texas.
a. W hat is the to ta l distance o f a trip fro m Tulsa to D allas to H ouston?
b. W h a t is th e t o t a l d is ta n c e o f a t r i p f r o m H o u s t o n t o D a lla s t o T u ls a?
c. E x p la in h o w y o u c a n t e l l w h e t h e r th e d is ta n c e s d e s c r ib e d i n p a r ts (a ) a n d ( b ) a re
e q u a l b y u s in g r e a s o n in g.
4ft See Problem 3.
(1 0 p )ll
1.1 + (7d + 0. 1 )
33xy
3x4f) See Problem 4.44.47.48.PowerAIgebra.com | Lesson 1-4 Properties o f Real NumbersTell whether the expressions in each pair are equivalent.- 2 + h + 4 a n d 2 • h • 4 39. 9 y • 0 a n d 1 40. 3x a n d 3x • 1
- m{ 1 — 1 ) a n d 0 42. (9 — 7) + 77 and 2v 43. (3 + 7) + m and m + 10
^|^and9ab 7 a 45. (2 + 5 - 7 ) and llx 4 6. 4 - -- 8 —— + V gr= an d7t
Think About a Plan H a n n a h m a k e s a l i s t o f p o s s ib le
gifts for M ary, Jared, and M ichael. She has tw o plans
a n d c a n s p e n d a t o t a l o f $ 7 5 f o r a ll g ifts. W h ic h p la n ( s )
can H annah afford?- W h a t p r o p e r t y c a n y o u u s e t o m a k e i t e a s ie r to f i n d
t h e t o t a l c o s t o f d if f e r e n t g ifts? - W h a t n u m b e r d o y o u c o m p a r e t o t h e t o t a l c o s t o f
e a c h p la n to d e c id e w h e t h e r i t is a ffo r d a b le?
Writing S u p p o s e y o u a re m ix in g r e d a n d b lu e p a i n t i n
a b u c k e t. D o y o u t h i n k th e f i n a l c o lo r o f t h e m ix e d p a i n t w i l l b e th e s a m e w h e t h e r
y o u a d d t h e b lu e p a in t o r t h e r e d p a i n t t o th e b u c k e t f ir s t? R e la te y o u r a n s w e r t o a
p r o p e r t y o f r e a l n u m b e r s.