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WorksheetsA1-Solving and Graphing Inequalities
Total questions: 164
Worksheet time: 8hrs 3mins
Name
Class
Date
1.
Solve the inequality.
x + 5 ≤ 13
x + 5 ≤ 13
a)
x ≥ 8
b)
x ≥ 18
c)
x ≤ 8
d)
x ≤ 18
2.
Solve the inequality.
x + 5 ≤ 13
x + 5 ≤ 13
a)
x ≥ 8
b)
x ≥ 18
c)
x ≤ 8
d)
x ≤ 18
3.
When you graph an inequality, you used a closed dot when you use which symbols?
a)
≤, ≥
b)
<, >
4.
When graphing an inequality, you use an open dot when you use which symbol?
a)
<, >
b)
≤, ≥
5.
In an equation or inequality, you want to get the variable...
a)
on one side
b)
to disappear
c)
isolated (by itself)
6.
Match the graph with its inequality.
a)
11 < a
b)
11 > a
c)
11 ≤ a
d)
11 ≥ a
7.
Will my dot be colored in?
5 ≥ x
5 ≥ x
a)
Yes
b)
No
8.
10 ≥ x - 3
a)
x ≤ 13
b)
x ≥ 13
c)
x ≤ 7
d)
x ≥ 7
9.
What are two solutions to x < 8?
a)
8.6, 7.9
b)
11, 16
c)
0.8, 5.9
d)
12, 7.1
10.
Does the given value make the inequality true? x + 9 > 21, when x = 15
a)
True
b)
Not True
11.
The maximum score on the pilot's test is 95 points.
a)
p < 95
b)
p > 95
c)
p ≥ 95
d)
p ≤ 95
12.
7 is less than a number.
a)
x > 7
b)
x < 7
c)
x ≤ 7
d)
x ≥ 7
13.
When graphing b < 6 would you use an open or closed circle?
a)
Open
b)
closed
14.
Which sentence represents m > 41?
a)
Mary’s points, m, totaled more than 41
b)
Calvin ran no less than 41 miles, m
c)
The temperature, m, was less than 41°F
d)
The magazines’ cost, m, was not more than $41.
15.
X - 10 > 25
a)
X > 35
b)
X < 35
c)
X > -35
d)
X < -35
16.
"At most" and "No more than" are both clue words for...
a)
<
b)
>
c)
≤
d)
≥
17.
The product of x and 7 is not greater than 10
a)
7x >10
b)
7x ≤ 10
c)
7 + x < 10
d)
7 / x < 10
18.
28 > m - 4
a)
m < 32
b)
m > 32
c)
m < 24
d)
m > 24
19.
Write an inequality for this situation:
You are driving, and the maximum speed limit is 55.
You are driving, and the maximum speed limit is 55.
a)
s < 55
b)
s > 55
c)
s ≤ 55
d)
s ≥ 55
20.
3g >12
a)
g>36
b)
g<36
c)
g>4
d)
g<4
21.
x/4≤8
a)
x≤2
b)
x≤32
c)
x≤12
d)
x≤4
22.
k/2≥8
a)
k≥16
b)
k≥6
c)
k≥4
d)
k≥10
23.
4h<8
a)
h<32
b)
h<2
c)
h<4
d)
h>2
24.
m - 5 > 10
a)
m is less than 15
b)
m is greater than 5
c)
m is greater than 15
d)
m is less than 5
25.
- 2k > 18
a)
k is greater than 20
b)
k is less than negative 9
c)
k is greater than negative 9
d)
k is less than 36
26.
8x ≥ -32
a)
x ≥ -4
b)
x ≥ 4
c)
x ≤ -4
d)
x ≥ 4
27.
s + 9 ≥ -25
a)
s ≥ -18
b)
s ≥ -34
c)
s ≤ 18
d)
s ≥ 34
28.
4x - 2 ≤ -22
a)
x ≥ -5
b)
x ≥ -6
c)
x ≤ -6
d)
x ≤ -5
29.
7b - 3 < 11
a)
b < 2
b)
84 > b
c)
b > 2
d)
b < 84
30.
6 - 2h > 30
a)
h < 24
b)
18 > h
c)
h > 12
d)
h < -12
31.
1 + 3r > 10
a)
r < 11
b)
r > 3
c)
27 > r
d)
r > 27
32.
-7 + 10z > -27
a)
z < -2
b)
z > -34
c)
2 > z
d)
z > -2
33.
more than
a)
<
b)
>
c)
≤
d)
≥
34.
Fewer Than
a)
<
b)
>
c)
≤
d)
≥
35.
No More Than
a)
<
b)
>
c)
≤
d)
≥
36.
At Least
a)
<
b)
>
c)
≤
d)
≥
37.
At Most
a)
<
b)
>
c)
≤
d)
≥
38.
less than or equal to
a)
<
b)
>
c)
≤
d)
≥
39.
Less Than
a)
<
b)
>
c)
≤
d)
≥
40.
Not Below
a)
<
b)
>
c)
≤
d)
≥
41.
Below
a)
<
b)
>
c)
≤
d)
≥
42.
No Fewer Than
a)
<
b)
>
c)
≤
d)
≥
43.
maximum
a)
<
b)
>
c)
≤
d)
≥
44.
Not Exceeding
a)
<
b)
>
c)
≤
d)
≥
45.
Above
a)
<
b)
>
c)
≤
d)
≥
46.
greater than or equal to
a)
<
b)
>
c)
≤
d)
≥
47.
is no less than
a)
<
b)
>
c)
≤
d)
≥
48.
minimum
a)
<
b)
>
c)
≤
d)
≥
49.
Not Above
a)
<
b)
>
c)
≤
d)
≥
50.
Exceeding
a)
<
b)
>
c)
≤
d)
≥
51.
Greater than
a)
<
b)
>
c)
≤
d)
≥
52.
26 < f + 32
a)
f > -6
b)
f < -6
c)
f < 6
d)
f < 55
53.
-8x < 48
a)
x < -6
b)
x > -6
c)
x < 6
d)
x > 6
54.
-4x + 14 ≤ 54
a)
x ≥ -10
b)
x ≤ -10
c)
x ≥ 10
d)
x ≤ 10
55.
10 < 3x + 19
a)
x < 3
b)
x > 3
c)
x < -3
d)
x > -3
56.
Match the graph with its inequality.
a)
11 < a
b)
11 > a
c)
11 ≤ a
d)
11 ≥ a
57.
Pick the correct inequality.
a)
A
b)
B
c)
C
d)
D
58.
Which inequality is represented by this graph?
a)
2.75 > d
b)
2.75 < d
c)
2.75 ≥ d
d)
2.75 ≤ d
59.
Pick the correct letter for:
6 > x
6 > x
a)
A
b)
B
c)
C
d)
D
60.
Pick the correct letter for:
6 > x
6 > x
a)
A
b)
B
c)
C
d)
D
61.
Pick the correct letter for:
6 > x
6 > x
a)
A
b)
B
c)
C
d)
D
62.
What inequality does the number line graph represent?
a)
-x + 4 ≥ -1
b)
-2x + 3 > -7
c)
-x + 1 < -4
d)
2x + 3 ≥ 13
63.
-4x + 14 ≤ 54
a)
x ≥ - 10
b)
x ≤ -10
c)
x ≥ 10
d)
x ≤ 10
64.
If Thomas spends $16, he will have less than $78. At least, how much money did Thomas have before he spent $16?
a)
$95
b)
$94
c)
$93
d)
$92
65.
Do I need to flip my sign?
3x ≥ 12
3x ≥ 12
a)
Yes
b)
No
66.
Will my dot be colored in?
5 ≥ x
5 ≥ x
a)
Yes
b)
No
67.
Which is the solution of k/-12 ≤ -7?
a)
-84 ≥ k
b)
k ≤ 84
c)
k ≥ 84
d)
k ≥ -84
68.
Solve
3.6 - 4.85a ≥ -6.1
3.6 - 4.85a ≥ -6.1
a)
2 ≤ a
b)
a ≤ 2
c)
-2 ≥ a
d)
a ≥ -2
69.
-8x < 48
a)
x < -6
b)
x > -6
c)
x < 6
d)
x > 6
70.
Choose the correct circle type ( open or closed) and the direction of the arrow.
x take away 5 is less than 8
x take away 5 is less than 8
a)
open circle at 8, arrow going right
b)
closed circle at 8, arrow going left
c)
open circle at 8, arrow going left
d)
closed circle at 8, arrow going right
71.
14 < -2a + 6 - 2a
a)
a > -2
b)
a < -2
c)
a > 2
d)
a < 2
72.
5z - 2 - 2z < 13
a)
z > 5
b)
z < 5
c)
z > 1
d)
z < 1
73.
-3 ≥ x - 1
a)
2 ≥ x
b)
4 ≥ x
c)
-4 ≥ x
d)
-2 ≥ x
74.
10 ≥ x - 3
a)
x ≤ 13
b)
x ≥ 13
c)
x ≤ 7
d)
x ≥ 7
75.
5x - 7 ≥ 8
a)
x ≥ 3
b)
x ≤ 3
c)
x = 3
d)
x ≠ 3
76.
9x - 3 > 6
a)
x > 1
b)
x < 1
c)
x ≥ 1
d)
x = 1
77.
11 + 3x ≤ 17
a)
x ≤ 2
b)
x = 2
c)
x < 2
d)
x ≥ 2
78.
4x - 12 ≥ 8
a)
x ≥ 5
b)
x > 5
c)
x ≠ 5
d)
x = 5
79.
Solve.
a)
x ≤ 14
b)
x < 14
c)
x ≥ 14
d)
x = 14
80.
7x - 3 > 18
a)
x > 3
b)
x > -3
c)
x < 3
d)
x = -3
81.
3x + 1 ≥ 7
a)
x ≥ 2
b)
x ≥ -2
c)
x = 2
d)
x > 2
82.
2x + 5 > 13
a)
x > 4
b)
x > -4
c)
x > 9
d)
x > -9
83.
Solve.
a)
x > -28
b)
x > 28
c)
x > -14
d)
x > 14
84.
The keywords "at most" are used with which of the following symbols?
a)
≤
b)
>
c)
<
d)
≥
85.
The keywords "at least" are used with which of the following symbols?
a)
≥
b)
≤
c)
>
d)
<
86.
The keywords "not equal to" are used with which of the following symbols?
a)
≠
b)
≤
c)
>
d)
<
87.
5 < x + 10
a)
-5 < x
b)
5 < x
c)
-15 < x
d)
15 < x
88.
x - 7 ≥ 4
a)
x ≥ 11
b)
x ≥ -11
c)
x ≥ 3
d)
x ≥ -3
89.
14 ≥ x - 8
a)
22 ≥ x
b)
-22 ≥ x
c)
6 ≥ x
d)
-6 ≥ x
90.
8x - 19 < 13
a)
x < 4
b)
x < -4
c)
x = 4
d)
x < -3/4
91.
6x + 7 ≤ -17
a)
x ≤ -4
b)
x = -4
c)
x ≤ 2
d)
x = -2
92.
Solve.
a)
x ≥ 4
b)
x ≥ -4
c)
x = 4
d)
x < 4
93.
7x - 1 < 6
a)
x < 1
b)
x < -1
c)
x < 5/7
d)
x < -5/7
94.
Which of the following symbols means "less than"?
a)
<
b)
>
c)
≤
d)
≥
95.
Which of the following symbols means "more than"?
a)
>
b)
<
c)
≤
d)
≥
96.
Which of the following symbols means "less than or equal to"?
a)
≤
b)
<
c)
>
d)
≥
97.
Which of the following symbols means "greater than or equal to"?
a)
≥
b)
≤
c)
>
d)
<
98.
Would you use a closed or open circle to graph x < 3?
a)
Closed
b)
Open
99.
What inequality does the number line graph represent?
a)
x ≤ 4
b)
x ≥ -4
c)
x < -4
d)
x < 4
100.
Solve and graph.
p - 3 > -8
p - 3 > -8
a)
A
b)
B
c)
C
d)
D
101.
Solve and graph.
k - 13 > -51
k - 13 > -51
a)
A
b)
B
c)
C
d)
D
102.
Solve and graph.
8a > -136
8a > -136
a)
A
b)
B
c)
C
d)
D
103.
If Mr. Estes has at least 20 students in his 3rd period class, which inequality represents this situation?
a)
x ≥ 20
b)
x > 20
c)
x ≤ 20
d)
x = 20
104.
Mrs. Stephens wants at most 2 students in her office at one time. Which answer choice portrays this situation?
a)
x ≠ 2
b)
x < 2
c)
x ≤ 2
d)
x = 2
105.
What inequality does the number line graph represent?
a)
x ≥ 3
b)
x > 3
c)
x < -3
d)
x ≤ -3
106.
When graphing b< 6 would you use an open or closed circle?
a)
Open
b)
closed
107.
Will my circle be colored in?
5 ≥ x
5 ≥ x
a)
Yes
b)
No
108.
Pick the correct inequality.
a)
A
b)
B
c)
C
d)
D
109.
Match the graph with its inequality.
a)
a > 11
b)
a < 11
c)
a ≥ 11
d)
a ≤ 11
110.
Which represents the word sentence as an inequality?
A number w is smaller than 5.
A number w is smaller than 5.
a)
w < 5
b)
w > 5
c)
w ≤ 5
d)
w ≥ 5
111.
Which inequality represents the below statement. I can have no more than 10 pieces of candy.
a)
x ≥ 10
b)
x > 10
c)
x ≤ 10
d)
x < 10
112.
<
a)
equal
b)
less than
c)
less than or equal to
d)
at least
113.
≤
a)
equal
b)
less than
c)
less than or equal to
d)
at least
114.
≥
a)
equal
b)
greater than
c)
greater than or equal to
d)
at most
115.
>
a)
equal
b)
greater than
c)
greater than or equal to
d)
at most
116.
≥
a)
equal
b)
more than
c)
greater than or less than
d)
no less than
117.
≠
a)
equal
b)
more than
c)
not equal to
d)
no less than
118.
at least
a)
<
b)
>
c)
≤
d)
≥
119.
Rory (r) is at most 30 years old
a)
r < 30
b)
r > 30
c)
r ≤ 30
d)
r ≥ 30
120.
you must be at least 48 inches to ride the roller coaster.
a)
x > 48
b)
x < 48
c)
x ≤ 48
d)
x ≥ 48
121.
"At most" and "No more than" are both clue words for...
a)
<
b)
>
c)
≤
d)
≥
122.
The product of x and 7 is not greater than 10
a)
7x >10
b)
7x ≤ 10
c)
7 + x < 10
d)
7 / x < 10
123.
a number less than 7
a)
x > 7
b)
x < 7
c)
x ≤ 7
d)
x ≥ 7
124.
x is less than 9
a)
x < 9
b)
x > 9
c)
x ≥ 9
d)
x ≤ 9
125.
Which represents the word sentence as an inequality?
A number n is at least 17.
A number n is at least 17.
a)
n < 17
b)
n > 17
c)
n ≤ 17
d)
n ≥ 17
126.
Write the phrase as an expression.
twice a number x plus 8 is greater than 12
twice a number x plus 8 is greater than 12
a)
2 + 8x < 12
b)
2x + 8 > 12
c)
2(x+8) ≠ 12
d)
8(2+x)
127.
5 less than the product of 7 and s is no more than 14
a)
7s - 5
≤ 14
≤ 14
b)
5 - 7 + s
≥ 14
≥ 14
c)
7(s - 5)
d)
5 - 7s
≠ 14
≠ 14
128.
4 plus the product of 6 and n is less than 10
a)
4 + 6n
< 10
< 10
b)
4 - 6 + n
> 10
> 10
c)
6m + n
≠ 5
≠ 5
d)
4 + 6 + n
≥ 3
≥ 3
129.
-8x < 48
a)
x < -6
b)
x > -6
c)
x < 6
d)
x > 6
130.
10 ≥ x - 3
a)
x ≤ 13
b)
x ≥ 13
c)
x ≤ 7
d)
x ≥ 7
131.
9x + 3 < 21
a)
x > 2
b)
x < 2
c)
x > 9
d)
x < 9
132.
-4x + 14 ≤ 54
a)
x ≥ - 10
b)
x ≤ -10
c)
x ≥ 10
d)
x ≤ 10
133.
10 < 3x + 19
a)
x < 3
b)
x > 3
c)
x < -3
d)
x > -3
134.
a)
x > 2
b)
x > 5
c)
x >15
d)
x > 50
135.
-2(x+2) < 14
a)
x < - 5
b)
x > -5
c)
x < -9
d)
x > -9
136.
Write an inequality:
7 is greater than or equal to the quotient of a number and -4
7 is greater than or equal to the quotient of a number and -4
a)
7 ≥ x ÷ -4
b)
7 ≥ -4 ÷ x
c)
7 > x ÷ 4
d)
7 + x ÷ -4
137.
Write an inequality:
Twice the difference of 18 and x is less than 10
Twice the difference of 18 and x is less than 10
a)
10 - 2(18-x)
b)
2(18÷x) < 10
c)
2(18-x) < 10
d)
10 < 2(18) - x
138.
Write an inequality:
Six fewer than four times a number is at most 2
Six fewer than four times a number is at most 2
a)
4x - 6 ≤ 2
b)
4x - 6 ≥ 2
c)
6 - 4x ≤ 2
d)
6 < 4x + 2
139.
a)
x is less than or equal to 2
b)
x < 2
c)
2 < x
d)
x is greater than 2
140.
a)
x > 1
b)
1 ≥ x
c)
x is greater than or equal to 1
d)
x is less than or equal to 1
141.
m - 5 > 10
a)
m is less than 15
b)
m is greater than 5
c)
m is greater than 15
d)
m is less than 5
142.
- 2k > 18
a)
k is greater than 20
b)
k is less than negative 9
c)
k is greater than negative 9
d)
k is less than 36
143.
8x ≥ -32
a)
x ≥ -4
b)
x ≥ 4
c)
x ≤ -4
d)
x ≥ 4
144.
s + 9 ≥ -25
a)
s ≥ -18
b)
s ≥ -34
c)
s ≤ 18
d)
s ≥ 34
145.
4x - 2 ≤ -22
a)
x ≥ -5
b)
x ≥ -6
c)
x ≤ -6
d)
x ≤ -5
146.
7b - 3 < 11
a)
b < 2
b)
84 > b
c)
b > 2
d)
b < 84
147.
6 - 2h > 30
a)
h < 24
b)
18 > h
c)
h > 12
d)
h < -12
148.
1 + 3r > 10
a)
r < 11
b)
r > 3
c)
27 > r
d)
r > 27
149.
-7 + 10z > -27
a)
z < -2
b)
z > -34
c)
2 > z
d)
z > -2
150.
Which is the solution of
-4 - 6m > -9m + 8?
-4 - 6m > -9m + 8?
a)
m < -4
b)
m > 4
c)
m < 15
d)
m > 36
151.
Which is a solution of
5(v + 3) - 10v > -10
5(v + 3) - 10v > -10
a)
v < 5
b)
V > 5
c)
V > -5
d)
v < -5
152.
Could x = - 5 be a solution to the inequality -6 < 3x + 9 < 21?
a)
yes
b)
no
154.
Solve the inequality for w:
-5(w - 4) < -5w - 15
-5(w - 4) < -5w - 15
a)
w > 15
b)
All real numbers are solutions
c)
w < 5
d)
No solutions to this inequality
154.
Solve the inequality for w:
-5(w - 4) < -5w - 15
-5(w - 4) < -5w - 15
a)
w > 15
b)
All real numbers are solutions
c)
w < 5
d)
No solutions to this inequality
155.
You take a trip to the bowling alley, where each game cost $2, plus you plan to spend $10 on food. You can spend at most $25. Which inequality models this scenario?
a)
2x + 10 ≥ 25
b)
2x + 10 > 20
c)
2x + 10 ≤ 25
d)
2x + 10 < 25
156.
Four times a number, increased by 6 is greater than 22. Which inequality models this scenario?
a)
4x - 6 > 22
b)
4x + 6 < 22
c)
4x + 6 ≥ 22
d)
4x + 6 > 22
157.
a)
1/7
b)
47/36
c)
7
d)
23
158.
10 + 45 ÷ 9 -(14 ÷ 2) =
a)
9
b)
7
c)
53
d)
18
159.
Solve the following:
-2 ⋅ (3 + 8 ÷ 4)2
-2 ⋅ (3 + 8 ÷ 4)2
a)
-16
b)
1.375
c)
4
d)
-50
160.
Solve for y:
8x + 4y= 16
8x + 4y= 16
a)
y = -8x + 16
b)
y = 2x -4
c)
y = -2x + 4
d)
y = -8x + 12
161.
Solve:
32 - 7x = -6(x + 3)
32 - 7x = -6(x + 3)
a)
50
b)
3
c)
-3
d)
-50
162.
2x + 5(y - 1) when x=8 and y=5
a)
20
b)
31
c)
36
d)
-4
163.
Brewster collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. Write and graph the equation for the total pounds, P, of aluminum cans after w weeks.
a)
P = 125w
b)
P = 100 + 25w
c)
P = 100w + 25
d)
P = 100 + 25
164.
Solve:
3x + 2 < -7 or -4x + 5 < 1
3x + 2 < -7 or -4x + 5 < 1
a)
x < -3 and x < 1
b)
x < -3 and x > 1
c)
x < -3 or x < 1
d)
x < -3 or x > 1
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