Name: ______________________
Class: _________________
Date: _________
Inequalities Test STUDY GUIDE
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which description is a correct way to solve the equation below?
d
+ 8.2 = 6.4
−3
a.
b.
c.
d.
Subtract 8.2 from both sides, then divide both sides by −3
Add 8.2 to both sides, then multiply both sides by −3
Subtract 8.2 from both sides, then multiply both sides by −3
Add 8.2 to both sides, then divide both sides by −3
Solve the inequality. Graph the solution.
____
____
2.
w
≥ −6.6
11
a.
w ≤ –72.6;
c.
w ≥ –0.6;
b.
w ≤ –0.6;
d.
w ≥ –72.6;
1
3. −8 < − x
2
a.
x < –16;
c.
x < 16;
b.
x > 16;
d.
x < 4;
1
ID: A
Name: ______________________
____
____
____
4.
ID: A
k
≤ 22
−10
a.
k ≤ –2.2;
c.
k ≤ –220;
b.
k ≥ –220;
d.
k ≥ 220;
5. 16 ≤
w
−4
a.
w ≤ –4;
c.
w ≥ 64;
b.
w ≥ –64;
d.
w ≤ –64;
6. 2 > b ÷ ( −3 )
a.
2
b<− ;
3
c.
b < −6;
b.
2
b>− ;
3
d.
b > −6;
2
Name: ______________________
____
____
____
ID: A
7. −2p > −16
8.
a.
p < 8;
c.
p < 32;
b.
p > 8;
d.
p > 32;
9
7
m ≤–
2
6
a.
m ≥–
7
;
27
c.
m ≥–
21
;
4
b.
m ≤–
7
;
27
d.
m ≤–
21
;
4
9. 2m ≤
7
3
a.
m≤
14
;
3
c.
m≥
7
;
6
b.
m≤
7
;
6
d.
m≥
14
;
3
3
Name: ______________________
ID: A
____ 10. 75 > 15c
____ 11.
a.
c > 5;
c.
c > 1125;
b.
c < 5;
d.
c < 1125;
z
+1 ≤ 7
2
a.
z ≤ 16;
c.
z < 12;
b.
z ≥ 12;
d.
z ≤ 12;
____ 12. 5t − 10 > 55
a.
t ≤ 9;
c.
t ≥ 13;
b.
t > 13;
d.
t ≤ 13;
____ 13. 3n − 9 ≥ 21
a.
n ≥ 10;
c.
n ≤ 4;
b.
n > 10;
d.
n ≤ 10;
4
Name: ______________________
ID: A
____ 14. 5(g + 5) ≤ 15
a.
g ≥ −2;
c.
g ≤ 2;
b.
g ≤ −2;
d.
g ≥ 2;
____ 15. 14 ≤
w
+6
−2
a.
w ≤ 16;
c.
w ≥ –16;
b.
w ≤ –16;
d.
w ≥ 16;
____ 16. −6 − 5g ≤ −56
a.
g ≤ 10;
c.
g ≤ 250;
b.
g ≥ 10;
d.
g ≥ 250;
5
Name: ______________________
ID: A
____ 17. −4 ÁÊË p − 5 ˜ˆ¯ > −36
a.
p > 14;
c.
p < 14;
b.
p < 4;
d.
p > 4;
____ 18. 7 −
m
≤6
6
a.
m ≤ 29;
c.
m ≤ 6;
b.
m ≥ 6;
d.
m ≥ 29;
Write the word sentence as an inequality.
2
____ 19. A number b multiplied by 11 is at most −3 .
3
11
2
a.
≤ −3
c.
b
3
2
b. 11b ≤ −3
d.
3
____ 20. A number x is no less than –42.
a. x ≤ −42
b. x > −42
c.
d.
6
2
3
2
11b ≥ −3
3
11b < −3
x < −42
x ≥ −42
Name: ______________________
ID: A
Write the word sentence as an inequality. Then solve the inequality.
____ 21. The product of 9 and a number is greater than 63.
a. 9x < 63; x < 7
c. 9x ≥ 63; x ≥ 7
b. 9x ≤ 63; x ≤ 7
d. 9x > 63; x > 7
____ 22. Which inequality is represented by the graph shown below?
a.
b.
x>3
x≥3
c.
d.
Short Answer
Solve the inequality. Graph the solution.
1. 3t − 1 < 8
2. −
k
− 5 ≤ −2
4
3. 3(x + 4) ≥ 12
7
x<3
x≤3
Name: ______________________
ID: A
Solve the inequality. Graph the solution.
4.
x
>4
−2
Write the word sentence as an inequality.
5. The children in the class are more than 10 years old.
6. To pass the test you must score at least 60 on the test.
7. The maximum cost is $35.
8. You need to score at least 1500 points on your new video game to obtain the high score. You get 300
points after completing each level. Write and solve an inequality to find the number of levels you must
beat in order to obtain the high score.
9. The perimeter of the rectangle is at least 12 inches. The area is no more than 27 inches. Write and solve
an inequality for each condition. Give two possible values for x.
10. Would an open circle or a closed circle be used in the graph of the inequality k ≤ 66? Explain.
8
Name: ______________________
ID: A
11. Do x ≥ 11 and 11 ≥ x represent the same inequality? Explain.
Write and solve an inequality that represents the value of x.
12. The base is less than the height.
13. The height is greater than or equal to the base.
14. Error Analysis Describe and correct the error in solving the inequality.
2.3 ≤ x + 7.6
2.3 − 7.6 ≥ x + 7.6 − 7.6
−5.3 ≥ x
x ≥ −5.3
15. You earn $6.50 per hour at your summer job. Write and solve an inequality that represents the number
of hours you need to work in order to buy a digital camera that costs $234.
16. You have $6.50 to make copies. Each copy costs $0.45. Write and solve an inequality that represents
the number of copies you can make.
9
ID: A
Inequalities Test STUDY GUIDE
Answer Section
MULTIPLE CHOICE
1. ANS: C
Feedback
A
B
C
D
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
The student divides by –3 instead of multiplies by –3.
The student adds 8.2 instead of subtracts 8.2.
Correct answer
The student adds 8.2 instead of subtracts 8.2 and divides by –3 instead of multiplies
by –3.
PTS:
NAT:
ANS:
NAT:
MSC:
ANS:
NAT:
MSC:
ANS:
NAT:
MSC:
ANS:
NAT:
ANS:
NAT:
ANS:
NAT:
ANS:
NAT:
MSC:
ANS:
NAT:
ANS:
NAT:
ANS:
NAT:
ANS:
NAT:
ANS:
NAT:
ANS:
NAT:
1
7.EE.4a
D
7.EE.4b
Knowledge
C
7.EE.4b
Knowledge
B
7.EE.4b
Knowledge
D
7.EE.4b
D
7.EE.4b
A
7.EE.4b
B
7.EE.4b
Knowledge
B
7.EE.4b
B
7.EE.4b
D
7.EE.4b
B
7.EE.4b
A
7.EE.4b
B
7.EE.4b
DIF:
KEY:
PTS:
KEY:
Level 1
REF: Ch 4 Standards Assessment
equation | solution of an equation MSC: Knowledge
1
DIF: Level 1
REF: Section 4.3
inequality | multiplication | division | graph
PTS: 1
DIF: Level 1
REF: Section 4.3
KEY: inequality | multiplication | division | graph
PTS: 1
DIF: Level 1
REF: Section 4.3
KEY: inequality | multiplication | division | graph
PTS:
KEY:
PTS:
KEY:
PTS:
KEY:
PTS:
KEY:
1
inequality
1
inequality
1
inequality
1
inequality
DIF: Level 1
REF: Section 4.3
| one-step | graph
MSC: Knowledge
DIF: Level 1
REF: Section 4.3
| one-step | graph
MSC: Knowledge
DIF: Level 1
REF: Section 4.3
| one-step | graph
MSC: Knowledge
DIF: Level 1
REF: Section 4.3
| multiplication | division | graph
PTS:
KEY:
PTS:
KEY:
PTS:
KEY:
PTS:
KEY:
PTS:
KEY:
PTS:
KEY:
1
inequality
1
inequality
1
inequality
1
inequality
1
inequality
1
inequality
DIF: Level 1
| one-step | graph
DIF: Level 1
| one-step | graph
DIF: Level 1
| two-step | graph
DIF: Level 1
| two-step | graph
DIF: Level 1
| two-step | graph
DIF: Level 1
|two-step | graph
1
REF:
MSC:
REF:
MSC:
REF:
MSC:
REF:
MSC:
REF:
MSC:
REF:
MSC:
Section 4.3
Knowledge
Section 4.3
Knowledge
Section 4.4
Knowledge
Section 4.4
Knowledge
Section 4.4
Knowledge
Section 4.4
Knowledge
ID: A
15. ANS:
NAT:
16. ANS:
NAT:
17. ANS:
NAT:
18. ANS:
NAT:
19. ANS:
NAT:
20. ANS:
NAT:
21. ANS:
NAT:
22. ANS:
B
7.EE.4b
B
7.EE.4b
C
7.EE.4b
B
7.EE.4b
B
7.EE.4b
D
7.EE.4b
D
7.EE.4b
D
PTS:
KEY:
PTS:
KEY:
PTS:
KEY:
PTS:
KEY:
PTS:
KEY:
PTS:
KEY:
PTS:
KEY:
1
inequality |
1
inequality |
1
inequality |
1
inequality |
1
inequality
1
inequality
1
inequality
DIF:
two-step
DIF:
two-step
DIF:
two-step
DIF:
two-step
DIF:
MSC:
DIF:
MSC:
DIF:
MSC:
Level 1
| graph
Level 1
| graph
Level 1
| graph
Level 1
| graph
Level 1
Knowledge
Level 1
Knowledge
Level 1
Knowledge
REF:
MSC:
REF:
MSC:
REF:
MSC:
REF:
MSC:
REF:
Section 4.4
Knowledge
Section 4.4
Knowledge
Section 4.4
Knowledge
Section 4.4
Knowledge
Section 4.1
REF: Section 4.1
REF: Section 4.3
Feedback
A
B
C
D
The student confuses the meaning of the symbols and excludes the number 3.
The student confuses the meaning of the symbols.
The student forgets to include 3.
Correct answer
PTS: 1
NAT: 7.EE.4b
DIF: Level 1
KEY: inequality
REF: Ch 4 Standards Assessment
MSC: Knowledge
SHORT ANSWER
1. ANS:
t < 3;
PTS: 1
DIF: Level 1
REF: Ch 4 Quiz 2 NAT: 7.EE.4b
KEY: inequality | Addition Property of Inequality | Division Property of Inequality
MSC: Knowledge
2. ANS:
k ≥ −12
PTS: 1
DIF: Level 1
REF: Ch 4 Quiz 2 NAT: 7.EE.4b
KEY: inequality | Addition Property of Inequality | Multiplication Property of Inequality
MSC: Knowledge
2
ID: A
3. ANS:
x≥0
PTS: 1
DIF: Level 2
REF: Ch 4 Test A NAT: 7.EE.4b
KEY: inequality | Subtraction Property of Inequality | Division Property of Inequality
MSC: Knowledge
4. ANS:
x < −8
PTS: 1
DIF: Level 1
REF: Ch 4 Quiz 2
KEY: Multiplication Property of Inequality | inequality
5. ANS:
a > 10
NAT: 7.EE.4b
MSC: Knowledge
PTS: 1
KEY: inequality
6. ANS:
s ≥ 60
DIF: Level 1
MSC: Knowledge
REF: Ch 4 Test A NAT: 7.EE.4b
PTS: 1
KEY: inequality
7. ANS:
c ≤ 35
DIF: Level 1
MSC: Knowledge
REF: Ch 4 Test B NAT: 7.EE.4b
PTS: 1
DIF: Level 1
KEY: inequality
MSC: Knowledge
8. ANS:
300x ≥ 1500; x ≥ 5 levels
REF: Ch 4 Test B NAT: 7.EE.4b
PTS: 1
DIF: Level 2
REF: Ch 4 Quiz 2
KEY: inequality | Division Property of Inequality
9. ANS:
2(3) + 2x ≥ 12, x ≥ 3; 3x ≤ 27, x ≤ 9;
Sample answer: x = 3, x = 5
NAT: 7.EE.4b
MSC: Application
PTS: 1
DIF: Level 2
REF: Ch 4 Test B NAT: 7.EE.4b
KEY: inequality | Subtraction Property of Inequality | Division Property of Inequality | perimeter
MSC: Comprehension
10. ANS:
An closed circle would be used because 66 is a solution.
PTS: 1
DIF: Level 1
KEY: inequality | concept check
REF: Section 4.1
MSC: Knowledge
3
NAT: 7.EE.4b
ID: A
11. ANS:
no; x ≥ 11 is all values of x greater than or equal to 11. 11 ≥ x is all values of x is less than or equal to 11.
PTS: 1
DIF: Level 1
KEY: concept check | inequality
12. ANS:
x + 13 < 24; x < 11
REF: Section 4.1
MSC: Knowledge
NAT: 7.EE.4b
PTS: 1
DIF: Level 2
KEY: inequality | application
13. ANS:
17 ≥ x + 5; x ≤ 12
REF: Section 4.2 NAT: 7.EE.4b
MSC: Application
PTS: 1
DIF: Level 2
REF: Section 4.2 NAT: 7.EE.4b
KEY: inequality | application
MSC: Application
14. ANS:
When the solution was rewritten with the variable on the left side, the inequality symbol was not
reversed.
2.3 ≤ x + 7.6
2.3 − 7.6 ≥ x + 7.6 − 7.6
−5.3 ≥ x
x ≤ −5.3
PTS: 1
DIF: Level 2
KEY: inequality | error analysis
15. ANS:
6.50t ≥ 234; t ≥ 36 h
REF: Section 4.2
MSC: Analysis
NAT: 7.EE.4b
PTS: 1
DIF: Level 2
REF: Section 4.3 NAT: 7.EE.4b
KEY: inequality | application
MSC: Application
16. ANS:
0.45n ≤ 6.50; n ≤ 14.44; You can make at most 14 copies.
PTS: 1
DIF: Level 2
KEY: inequality | application
REF: Section 4.3 NAT: 7.EE.4b
MSC: Application
4