Download AT2_Review_Answers big

ALGEBRA2
REVIEW CHAPTER 2
NAME______________
SOLVE AND GRAPH EACH INEQUALITY
1) 13y  20+3y
2) 8y+7 ≤ 7-7y
10y>20
15y+7≤ 7
y>2
15y≤ 0
y≤ 0
3) 8(2-y) < 7y-14
16-8y<7y-14
16<15y-14
30<15y
2<y or y>2
5) -3  2y-9  15
6) 1 ≤ 3y or 2y+4  -8
6<2y<24
⅓≤ y
2y<-12
3<y<12
y≥ ⅓ or y<-6
4) 5y-4 < 3y
2y-4<0
2y<4
y<2
7) 3  3x-6  30
9>3x>36
3>x>12 false No Solution
8) 3y+7 ≤ 13 or 5y+3  38
3y≤ 6
5y>35
y≤ 2
or y>7
SOLVE AND GRAPH THE SOLUTION SET:
9)  x-3  ≤ 4
-4≤ x-3≤ 4
-1≤ x≤ 7
10) 7+3x =5
7+3x=5 or 7+3x=-5
3x=-2
3x=-12
x=-2/3 or x=-4
11)  ⅓ X-5  2
⅓x-5>2 or ⅓x-5<-2
⅓x>7 ⅓x<3
x>21 or x<9
12)  3x-2  -5  7
 3x-2 <12 -12<3x-2<12
-10<3x<14
-10/3<x<14/3
13) A store buys books for $3.95 each and sells them at $8.25 each. How
many must be sold to make a profit of no less than $300?
Let x= books
(8.25-3.95)x≥ 300
4.3x≥ 300
x≥ 69.8
70 Books
(OVER)
14) Find all sets of five consecutive even integers whose sum is between
200 and 230.
x,x+2,x+4,x+6,x+8
st
Let x= 1 even int
200<x+x+2+x+4+x+6+x+8<230 {38,40, 42, 44, 46}
nd
x+2= 2
200<5x+20<230
{40,42, 44, 46, 48}
rd
x+4=3
180<5x<210
th
x+6=4
36<x<42
x+8=5th
GIVE REASONS FOR THE STEPS IN THE PROOF:
15) IF g  0, h  0, and 1 = 1 , then g=h
g h
a) g  0, h  0 , 1 = 1
a) given
g h
b) gh = gh
b) Reflexive Property of Equality
c) (gh) 1 = (gh) 1
g
h
d) (gh) 1 = g(h 1 )
g
h)
e) (gh) 1 = g(1 )
g
f) (gh) 1 = g
g
.
g) (hg) 1=g
g
h) h(g.1 )=g
g
i) h(1)=g
j) h=g
k) g=h
c) Multiplication Property of Equality
d) Associative Property of Mult.
e) Property of Reciprocals
f) Identity Property of Multiplication
g) Commutative Property of Mult.
h) Associative Property of Multiplication
i) Property Of Reciprocals
j) Identity Property of Multiplication
k) Symmetric Property of Equality
16) What is the converse of this statement? Is the original statement true or
false? Is the converse true or false?
"If the absolute value of a number is positive then the number is positive.”
False │-2│=2 but -2 is not positive
Converse: If a number is positive then the absolute value of a number is
positive. True