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Systems of Inequalities 1

Total questions: 114

Worksheet time: 10hrs 30mins

Name
Class
Date
1.
Will my line be solid?
5 ≥ x
a)
Yes
b)
No
2.
Will my line be solid?
5 ≥ x
a)
Yes
b)
No
3.
Which point below is NOT part of the solution set?
a)
(0, 0)
b)
(5, 1)
c)
(-1, -3)
d)
(20, -5)
4.
Select the correct graph for each inequality.
a)
A
b)
B
c)
C
d)
D
5.
Select the correct graph for each inequality.
a)
A
b)
B
c)
C
d)
D
6.
Is (-2,4) a solution to the system?
a)
Solution
b)
Not a solution
7.
Which point is a solution?
a)
(0, 6)
b)
(-3, 4)
c)
(1, 0)
d)
(-4, 3)
8.
Which of the following is not a solution to this system of inequalities?
a)
(0,-1)
b)
(0,3)
c)
(4,0)
d)
(6,-2)
9.
Is (0,0) a solution to the system?
a)
Solution
b)
Not a solution
10.
Which of the following inequalities matches the given graph?
a)
x ≥ -1
b)
x ≤ -1
c)
x > -1
d)
x < -1
11.
Which point is a solution?
a)
(0, 6)
b)
(-3, 4)
c)
(1, 0)
d)
(-4, 3)
12.
Select the correct graph for each inequality.
a)
A
b)
B
c)
C
d)
D
13.
Is (0,0) a solution to the system?
a)
Solution
b)
Not a solution
14.
Is (-2,4) a solution to the system?
a)
Solution
b)
Not a solution
15.
Match the system to the graph (solution set is on the left)
a)
y ≤ 3x   and  y ≤ -2x + 4
b)
y > 3x   and  y > -2x + 4
c)
y < 3x   and  y > -2x + 3
d)
y > 3x   and  y < -2x + 4
16.
Which of the following is not a solution to this system of inequalities?
a)
(0,-1)
b)
(0,3)
c)
(4,0)
d)
(6,-2)
17.
Which system of inequalities matches the graph?
a)
y > 2x - 4
y < 2
b)
y < 2x - 4
y < 2
c)
y > 2x - 4
y <  2 
d)
y < 2x - 4
y <   -2
18.
Which of the following points is a solution to the system of equations below?
x + 2y ≥ 4
3x − 2y < 4
Take your time!
a)
(0, 0)
b)
(2, 1)
c)
(2, 2)
d)
(-1, 1)
19.
Which system of inequalities is shown?
a)
y ≥ -x - 1
y < x + 4
b)
y < -x - 1
 y ≥ x + 4
c)
y > -x - 1
y ≥ x + 4
d)
y > -x - 1
y ≥ x + 3
20.
Which point below is NOT part of the solution set?
a)
(0, 0)
b)
(5, 1)
c)
(-1, -3)
d)
(20, -5)
21.
David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. 
a)
35 nachos, 52 sodas
b)
18 nachos, 69 sodas
c)
52 nachos, 35 sodas
d)
61 nachos, 26 sodas
22.
Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. How many of each type of ticket were sold?
a)
10 adults, 11 children
b)
12 adults , 9 children
c)
11 adults, 10 children
d)
9 adults, 12 children
23.
The length of a rectangle is 3 times the width. The perimeter of the rectangle is 72 feet. What is the area of the rectangle?
a)
243
b)
36
c)
9
d)
24
24.
Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing
a)
x+y≤300
7.5x+5.5y≥2000
b)
x+y<300
7.5x+5.5y≥2000
c)
x+y≤300
7.5x+5.5y≤2000
d)
x+y>2000
7.5x+5.5y≤300
25.

Solve the system of inequalities by graphing.

a)
b)
c)
d)
26.

Solve the system of inequalities by graphing.

a)
b)
c)
d)
27.
Write an inequality represented by the graph.
a)
x < - 3
b)
y < - 3
c)
x > - 3
d)
x ≥ - 3
28.
Write an inequality represented by the graph.
a)
x < - 3
b)
y < - 3
c)
x > - 3
d)
x ≥ - 3
29.
An inequality using a > or a < has a ___________ line
a)
invisible
b)
solid
c)
dashed
30.
Will my line be solid?
5 ≥ x
a)
Yes
b)
No
31.
The graph of 
y ≥  x - 3 
is shaded ???
a)
Over / Above
b)
Under / Below
32.
Which system of inequalities matches the graph?
a)
x> -2
y < -4
b)
x< 2
y> 4
c)
x >  2
y <  4  
d)
x > 2
y <- 4
33.
Which system of inequalities matches the graph?
a)
x> -2
y < -4
b)
x< 2
y> 4
c)
x >  2
y <  4  
d)
x > 2
y <- 4
34.
Which system of inequalities matches the graph?
a)
x> -2
y < -4
b)
x< 2
y> 4
c)
x >  2
y <  4  
d)
x > 2
y <- 4
35.

Solve the system of inequalities by graphing.

a)
b)
c)
d)
36.

Which inequality matches the graph?

a)

x<3

b)

x>3

c)

x<3

d)

x>3

37.

Which scenario could be represented by the graph?

a)

The temperature is less than -1 degree.

b)

The temperature is more than -1 degree.

c)

The temperature is at most -1 degree.

d)

The temperature is at least -1 degree.

38.

Which inequality matches the graph?

a)

x>-2

b)

x<-2

c)

x>-2

d)

x<-2

39.

Mr. Gomez gets a notice from the bank when the amount in his checking account drops below $20. Which represents an amount that will require the bank to send a notice?

a)

$18

b)

$19

c)

$20

d)

$21

e)

$22

40.

Mr. Gomez gets a notice from the bank when the amount in his checking account drops below $20. Which inequality represents when Mr. Gomez will receive a notice from the bank?

a)

x<20

b)

x>20

c)

x>20

d)

x<20

41.

You must spend at least $10 at the grocery store to get a free reusable shopping bag. Which inequality represents the amount you need to spend to get a free shopping bag?

a)

x<10

b)

x>10

c)

x>10

d)

x<10

42.

Antavius must score at least 4 more points in the game this weekend than he did in the last game to be the top scorer for his team. In the last game he scored 13 points. Which inequality represents what Antavius must score, s, to be the team's top scorer?

a)

s>4

b)

s>13

c)

s>17

43.

Andy runs the same number of miles, x, every day. His total distance run for one week is less than 60 miles. Which inequality represents how many miles Andy runs each day?

a)

7 + x > 60

b)

7 + x < 60

c)

7x>60

d)

7x<60

44.

When the following inequality is graphed, what will it look like?


y>-1

a)

open circle

b)

closed circle

45.

When the following inequality is graphed, what will it look like?


y<5

a)

open circle

b)

closed circle

46.

When the following inequality is graphed, what will it look like?


z < - 1/2

a)

open circle

b)

closed circle

47.

When the following inequality is graphed, what will it look like?


r < -12.97

a)

open circle

b)

closed circle

48.

When the following inequality is graphed, what will it look like?


5.0825 < c

a)

open circle

b)

closed circle

49.

When the following inequality is graphed, what will it look like?


"Kelsey has at most 10 dollars"

a)

open circle

b)

closed circle

50.

When the following inequality is graphed, what will it look like?


5.0825 < c

a)

open circle

b)

closed circle

51.

When the following inequality is graphed, what will it look like?


"Kelsey has at most 10 dollars"

a)

open circle

b)

closed circle

52.

When the following inequality is graphed, what will it look like?


"Alex will spend less than 35 minutes playing video games"

a)

open circle

b)

closed circle

53.

When the following inequality is graphed, what will it look like?


"Alex will spend less than 35 minutes playing video games"

a)

open circle

b)

closed circle

54.
8 ( x + 2) = ?
a)
8x + 2
b)
8x + 16
c)
24x
d)
6
55.
4 ( x + 3) = ?
a)
4x + 3
b)
4x + 12
c)
7x
d)
16x
56.
5( 2x + 3) = ?
a)
10x + 3
b)
7x + 8
c)
10x + 15
d)
25x
57.
-8 ( x + 2) = ?
a)
-8x + 2
b)
-8x + 16
c)
-8x – 16
58.

-8 ( x – 2) = ?

a)

-8x + 2

b)

-8x + 16

c)

-8x – 16

59.
-4 ( x + 3) = ?
a)
-4x + 3
b)
-4x + 12
c)
-4x – 12
60.

-4 ( x – 3) = ?

a)

-4x + 3

b)

-4x + 12

c)

-4x – 12

61.
-5( 2x + 3) = ?
a)
-10x + 3
b)
-10x + 15
c)
-10x – 15
62.
-5( 2x – 3) = ?
a)
-10x + 3
b)
-10x + 15
c)
-10x – 15
63.
My very first step is to ALWAYS distribute in algebra problems where I see a number being multiplied by what is inside the parentheses: What does this simplify to?  -1/2(4t - 2) = 8 
a)
-2t + 1 = 8
b)
-2t - 1 = 8
c)
2t - 1 = 8
d)
2t + 1 = 8
64.
My very first step is to ALWAYS distribute in algebra problems where I see a number being multiplied by what is inside the parentheses: What does this simplify to?  -1/3(9t - 6) = -30 
a)
-3t + 2 = -30
b)
-3t - 3 = -30
c)
3t - 2 = -30
d)
3t + 3 = -30
65.
My very first step is to ALWAYS distribute in algebra problems where I see a number being multiplied by what is inside the parentheses: What does this simplify to?  -1/5(-5t + 10) = -7 
a)
t + 2 = -7
b)
-t - 2 = -7
c)
t - 2 = -7
d)
-t - 2 = -7
66.
My very first step is to ALWAYS distribute in algebra problems where I see a number being multiplied by what is inside the parentheses: What does this simplify to?  -1/5(-1/5t + 2/10) = 1
a)
1/25t - 2/50 = 1
b)
-1/25t + 2/50 = 1
c)
-1/25t - 2/50 = 1
d)
1/25t + 2/50 = 1
67.
My very first step is to ALWAYS distribute in algebra problems where I see a number being multiplied by what is inside the parentheses: What does this simplify to?  1/3(1/2t + 2/5) = 1
a)
1/6t + 2/15 = 1
b)
1/5t + 3/8 = 1
c)
1/5t + 2/15 = 1
d)
1/6t + 3/15 = 1
68.
4(9 + 11g)
a)
36 + 44g
b)
49 + 44g
c)
13 + 15g
d)
36 + 15g
69.
7(9n - 2)
a)
16n -14
b)
63n - 14
c)
63n + 7
d)
16n - 14
70.
- (6 + 7d)
a)
6 + d
b)
-6 + -d
c)
13d
d)
-6 - 7d
71.
-8(3 + 4w)
a)
-5 + -4w
b)
-24 - 4w
c)
-24 + -32w
d)
-11 + -12w
72.
100(2 - 4a)
a)
200a
b)
102 + 4a
c)
102 - 4
d)
200 - 400a
73.

0.23 + 0.4

a)

0.63

b)

0.27

c)

4.23

d)

0.234

74.

0.73 + 0.02

a)

0.75

b)

0.93

c)

0.732

d)

1.03

75.

0.61 + 0.7

a)

1.31

b)

0.68

c)

0.617

d)

1.41

76.

0.625 + 0.34

a)

0.965

b)

0.659

c)

0.929

d)

0.6284

77.

0.32 + 0.004

a)

0.324

b)

0.36

c)

0.72

d)

0.82

78.

0.007 + 0.85

a)

0.857

b)

0.92

c)

0.82

d)

1.55

79.

0.304 + 0.05

a)

0.354

b)

0.854

c)

0.804

d)

0.309

80.

1.37 + 0.5

a)

1.87

b)

6.37

c)

1.32

d)

1.42

81.

2.3 + 0.06

a)

2.36

b)

2.9

c)

2.306

d)

2.306

82.

31.5 + 6.24

a)

37.74

b)

93.9

c)

32.124

d)

30.74

83.

86.5 + 4.83

a)

91.33

b)

90.33

c)

96.33

d)

80.63

84.

4.87 + 18.2

a)

23.07

b)

22.07

c)

23.87

d)

22.87

85.
List all the factors of 12
a)
1, 2, 3, 4, 6, 12
b)
1, 2, 4, 12
c)
1, 12
d)
1, 2, 3, 4, 5, 6, 12
86.
What are the factors of 25?
a)
1, 2, 3, 5, 10, 15, 25
b)
1, 5,  25
c)
1, 25
d)
1, 5
87.
What is the greatest common factor of the monomials a2b5 and a3b3
a)
a2b3
b)
a2b5
c)
a3b3
d)
a3b5
88.
What is the Greatest Common Factor of the following polynomial?
12t3 + 30t2 + 48t
a)
12t
b)
6t3
c)
6t
d)
12t3
89.
Find the greatest common factor of
6x4y3 - 12x4y2 + 6x3y2
a)
6
b)
6xy
c)
6x3y2
d)
6x9y6
90.
What is the GCF of 18k and 15k3
a)
3k2
b)
3k3
c)
3k
d)
5k
91.
Determine the greatest common factor of 
-5j3k7m2 and -20jk2m5
a)
-5jk2m2
b)
-20j3k7m5
c)
-5j3k7m5
d)
-20jk2m2
92.

"The distance a number is from zero on a number line" is defined as:

a)

integer

b)

negative

c)

operation

d)

absolute value

93.
What is the absolute value of |-99|.
a)
99
b)
-99
c)
0
d)
It doesn't have one
94.

− | -13 | =

a)

0

b)

13

c)

undefined

d)

− 13

95.

4 + (-5) =

a)

9

b)

-9

c)

1

d)

-1

96.

15 - 10 =

a)

25

b)

5

c)

-5

d)

-25

97.

-15 + 8

a)

-7

b)

-6

c)

-5

d)

-8

98.

-7 + - 3 =

a)

10

b)

-4

c)

4

d)

-10

99.

10 - (-7) =

a)

3

b)

7

c)

17

d)

-17

100.
A negative divided by a negative is a ________
a)
positive
b)
negative
101.
A negative multiplied by a negative is a ________
a)
positive
b)
negative
102.
A negative divided by a negative is a ________
a)
positive
b)
negative
103.
A negative multiplied by a negative is a ________
a)
positive
b)
negative
104.
A negative multiplied by a positive is a ________
a)
positive
b)
negative
105.
-5 x 2 = 
a)
-3
b)
-10
c)
-15
d)
10
106.
-7 x  (-11)  = 
a)
77
b)
-18
c)
-77
d)
-70
107.
-12 x 0 =
a)
-129
b)
-1
c)
129
d)
0
108.
9 x  (-6) = 
a)
-63
b)
3
c)
-54
d)
54
109.
5 x (-7) =
a)
-35
b)
-48
c)
48
d)
56
110.
-10 x 3 = 
a)
-9
b)
3
c)
-1
d)
-30
111.
10 x (-2) =
a)
-20
b)
20
c)
8
d)
-5
112.
(-7) x (-3) =
a)
-21
b)
21
c)
-3
d)
-7
113.
-14 ÷ 7 = 
a)
-2
b)
2
c)
98
d)
-98
114.
−27 ÷ −9 =
a)
3
b)
-3
c)
243
d)
-243

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