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Solve. Write your answer
in interval notation.
3(2 x  1)  2( x  4)  7  2(3  4 x)
1
3(2 x  1)  2( x  4)  7  2(3  4 x)
6x  3  2x  8  7  6  8x
4 x  5  8 x  13
5  4 x  13
8  4 x
2  x
x  2
(, 2]
1
Solve for x.
2x
x
 6
3
4
1
2x
x
 6
3
4
LCD  (3)(4)  12
x
 2x  
(12)     6   (12)
4
 3  
4(2 x)  6(12)  x(3)
8 x  72  3 x
11x  72
72
x
11
1
Solve for x.
5
1
8

 2
x3 x2 x  x6
1
5
1
8

 2
x3 x2 x  x6
5
1
8


x  3 x  2 ( x  3)( x  2)
LCD  ( x  3)( x  2) x  3, x  2

1  
8
 5
( x  3)( x  2) 

 ( x  3)( x  2)

 x  3 x  2   ( x  3)( x  2) 
5( x  2)  1( x  3)  8
5 x  10  x  3  8
6x  7  8
6 x  15
15 5
x 
6 2
1
Solve. Write your answer
in interval notation.
5  2 x  1  3
1
5   2 x  1  3
6  2 x  2
3  x  1
[1,3)
1
Solve for x.
x  3 1 x 1
 
2 x  2 6 3x  3
1
x  3 1 x 1
x 3
1
x 1
 

 
2 x  2 6 3x  3
2( x  1) 6 3( x  1)
x 3
1 1
x 3
1
  

2( x  1) 6 3
2( x  1) 2
LCD  6( x  1) x  1
 x 3   1 
6( x  1) 
    6( x  1)
 2( x  1)   2 
3( x  3)  3( x  1)
x  3  x 1
3  1
no solution
1
Solve
3 x4 7 8
2
3 x4 7 8
3 x  4  15
x4 5
x  4  5 or x  4  5
x9
check!
or x  1
2
Solve. Write your answer
in interval notation.
2x  3  5  0
2
2x  3  5  0
2x  3  5
2 x  3  5 or 2 x  3  5
2 x  8 or 2 x  2
x  4 or x  1
(, 1) (4, )
2
Solve
5x  6  x
2
5x  6  x
5x  6  x
2
x  5x  6  0
2
( x  2)( x  3)  0
x  2 or x  3
check!
2
Solve. Write your answer
in interval notation.
1
3 x 1  6  0
2
2
1
3 x 1  6  0
2

1
3 x 1  6
2
1
x 1  2
2
1
2  x  1  2
2
1
3  x  1
2
6  x  2
[6, 2]
2
Solve
x3  x4  2
2
x3  x4  2
x3  x4 2
x3 x44 x4 4
x3 x4 x4
3 4 x4
3
 x4
4
9
 x4
16
73
x
check!
16
2
Simplify
(2  3i)(1  5i)
3
(2  3i )(1  5i)  2  10i  3i  15i
2
 2  13i  15(1)
 2  13i  15
 13  13i
3
Simplify
2  6i
5  3i
3
2  6i (2  6i) (5  3i)

5  3i (5  3i ) (5  3i )
10  6i  30i  18i

25  9
10  36i  18

34
8  36i

34
8 36

 i
34 34
4 18

 i
17 17
2
3
Simplify and write in
standard form.
3

3  6

3
3



3  6  i 3 i 3  6
i
2

33  i 3 6
 (1)(3)  i  3 2
 3  3i 2
3
Solve
x
2/3
x
1/ 3
20
3
x 2 / 3  x1/ 3  2  0
( 13 )2 
2
3
( x1/ 3 ) 2  x1/ 3  2  0
let u  x
1/ 3
u2  u  2  0
(u  2)(u  1)  0
u  2  0 or u  1  0
u  2 or u  1
x1/ 3  2 or x1/ 3  1
( x1/ 3 )3  (2)3 or (x1/ 3 )3  ( 1)3
x  8 or x  1
check
3
Solve.
x  4 x  13  0
2
3
completing the square
quadratic formula
x  4 x  13  0
x 2  4 x  13  0
a  1, b  4, c  13
2
x  4 x  13
2
( b2 ) 2  ( 24 ) 2  ( 2) 2
x 2  4 x  (2) 2  13  4
( x  2) 2  9
x  2   9
x  2  3i
x  2  3i
(4)  (4)  4(1)(13)
x
2(1)
2
4  16  52

2
4  36 4  6i


2
2
4 6i
 
2 2
x  2  3i
3
Solve.
(5  3x)  7  0
2
3
(5  3 x)  7  0
2
(5  3 x)  7
2
5  3x   7
3 x   5  7
5  7
x
3
3
Write the equation of the
circle in standard form.
Give the center and radius.
x  y  8x  6 y  24  0
2
2
4
x  y  8 x  6 y  24  0
2
2
( x  8 x)  ( y  6 y )  24
2
2
for the x group: ( )  ( )  ( 4)  16
8 2
2
b 2
2
2
for the y group: ( )  ( )  (3)  9
b 2
2
6 2
2
2
( x  8 x  (4) )  ( y  6 y  (3) )  24  16  9
2
2
2
2
( x  4)  ( y  3)  49
center: (4, 3)
2
radius:
2
49  7
4
Given the equation of the
circle, identify the center
and radius, and sketch the
graph.
( x 1)  y  4
2
2
4
( x  1)  y  4
2
2
center: (1, 0)
4 2
radius:
y
4
2
x
5
4
3
2
1
1
2
3
4
5
2
4
4
Find the distance between
the points.
(1, 2) and (4,1)
4
(1, 2) and (4,1)
d  (1  4)  (2  1)
2
2
 (5)  (3)  25  9  34
2
2
OR
d  (4  (1))  (1  (2))
2
2
 (5)  (3)  25  9  34
2
2
4
Write the equation of the
circle in standard form given
the center of (1, 6) and
radius of 5.
4
center : (1, 6)
r 5
( x  h)  ( y  k )  r
2
2
( x  1)  ( y  6)  5
2
2
2
2
( x  1)  ( y  6)  25
2
2
4
Find the midpoint of the
line segment connected
by the points
( , 1) and ( , 4)
1
2
9
2
4
( , 1) and ( , 4)
9
2
1
2
  1  (4) 
midpt  
,

2
 2

10
 2 5   5 5 
  ,    ,   (2.5, 2.5)
 2 2  2 2 
1
2
9
2
4
Graph the line using intercepts
2x  3y  6  0
5
2x  3y  6  0
x  int :
2 x  3(0)  6  0
2 x  6
x  3
y  int :
y
6
4
2
x
5
4
3
2
1
1
2
3
4
5
2
4
6
2(0)  3 y  6  0
3 y  6
y  2
5
Write the equation in slope
intercept form of the line
passing through the point (3, 6)
and perpendicular to the line
y  x4
1
3
5
y  x  4, m 
1
3
1
3
So the slope of our line is m  3,
and we have the point (3, 6)
y  6  3( x  3) (pt-slope form)
y  6  3x  9
y  3x  3 (slope-int form)
5
Identify the slope of each equation as
positive, negative, zero, or undefined.
Then classify the equation as increasing,
decreasing, horizontal, or vertical.
a) x 
1
2
b) y  x  3
2
5
c) y  6
d) y  4 x  10
5
a) x 
1
2
slope undefined, vertical line
b) y  x  3
2
5
positive slope, increasing graph
c) y  6
zero slope, horizontal line
d) y  4 x  10
negative slope, decreasing graph
5
Write the equation of the line
in point-slope form for the
line passing through (4,-7)
and parallel to the line
2x  y  4  0
5
2x  y  4  0
y  2 x  4, m  2
our line has m  2 and point (4, 7)
y  (7)  2( x  4)
y  7  2( x  4)
5
Test the equation for
symmetry across the x-axis,
y-axis, and the origin.
5x  2 x  4 y
2
2
5
5x  2 x  4 y
2
2
x  axis :
5 x  2 x 2  4( y ) 2
5 x  2 x  4 y  sym across x  axis
2
2
y  axis :
5( x)  2( x)  4 y
2
2
5 x  2 x 2  4 y 2  no sym across y  axis
origin :
5( x)  2( x)  4(  y )
2
2
5 x  2 x  4 y  no sym thru origin
2
2
5
Write the equation of the
line passing through points
(2, 5) and (3, 0)
5
(2, 5) and (3, 0)
5  0 5
m

5
2  3 1
point-slope form:
y  0  5( x  3) or y  5  5( x  2)
slope-intercept form:
y  5 x  15
standard form:
5 x  y  15 or  5 x  y  15
5
A car rental agency charges
$20 per day and $0.12 per mile.
How many miles can be driven
to have a cost of at least $32
and at most $44?
6
Let x  number of miles driven
32  20  0.12 x  44
12  0.12 x  24
100  x  200
The number of miles driven should be
between 100 and 200, inclusive.
6
You invest a total of $6,000 into a
savings account and a money
market account. The savings
account earns 2% annual interest
and the money market account
earns 5% annual interest. If you
earn $255 in interest, how much
money did you have in each account.
6
x  interest earned in savings acct
6000  x  interest earned in money market acct
0.02 x  0.05(6000  x)  255
0.02 x  300  0.05 x  255
0.03x  300  255
0.03x  45
x  1500
6000  x  6000 1500  4500
$1500 in savings
$4500 in money market
6
The length of Pam’s living room
is 5m less than 2 times the width
of the room. If the perimeter of
the room is 70m, what are the
dimensions of the living room?
6
x  width of living room
2 x  5  length of the living room
P=2length+2width
70  2(2 x  5)  2 x
70  4 x  10  2 x
70  6 x  10
80  6 x
80
x
6
13.3  x
width is 13.3 ft
length is 2(13.3)-5=21.6 ft
6
The area of a rectangular garden
is 1120 square feet. The length
of the garden is 4 less than 3 times
the width. Find the dimensions of
the garden.
6
x  width
3x  4  length
area  (length)( width)
1120  x(3 x  4)
1120  3x 2  4 x
0  3x 2  4 x  1120
0  ( x  20)(3 x  56)
x  20  0
or
3 x  56  0
56
x  20
or x 
can't have negative width
3
so width is 20 ft and length is 3(20)  4  56 ft
6
Gym A charges $10 for a membership
plus $1 per visit. Gym B charges $5
for a membership plus $1.50 per visit.
After how many visits will the costs
be the same? What is the cost?
6
x  # visits
Gym A cost = Gym B cost
10  1x  5  1.5 x
5  x  1.5 x
5  0.5 x
10  x
The cost is the same after 10 visits.
The cost will be 10  1(10)  $20
or could use 5  1.5(10)  $20
6