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Solving Inequalities (using Addition and Subtraction) Worksheet

Solving Inequalities (using Addition and Subtraction) Worksheet
  • Page 1
 1.  
Which of the following is a solution to the inequality, n + 3 > 49?
a.
44
b.
49
c.
43
d.
41


Solution:

A solution of the inequality is any value of the variable that makes the inequality true.

n + 3 > 49
[Original inequality.]

n + 3 - 3 > 49 - 3
[Subtract 3 from each side.]

n > 46
[Simplify.]

Among the choices, 49 is the only number that is a solution of the inequality n + 3 > 49.


Correct answer : (2)
 2.  
Solve the inequality.
x - 0.7 ≤ 2.1
a.
x ≤ -2.8
b.
x ≥ 2.8
c.
x ≤ 2.8
d.
x ≥ -2.8


Solution:

x - 0.7 ≤ 2.1
[Original inequality.]

x - 0.7 + 0.7 ≤ 2.1 + 0.7
[Add 0.7 to each side.]

x ≤ 2.8
[Simplify.]


Correct answer : (3)
 3.  
Which of the following choices is a solution of the inequality, n + 4 < 74?
a.
74
b.
68
c.
74
d.
72


Solution:

A solution of the inequality is any value of the variable that makes the inequality true.

n + 4 < 74
[Original inequality.]

n + 4 - 4 < 74 - 4
[Subtract 4 from each side.]

n < 70
[Simplify.]

Among the choices, 68 is the only number that is a solution of the inequality n + 4 < 74.


Correct answer : (2)
 4.  
Which of the following choices is the solution for the inequality, n - 5 > 26?
a.
27
b.
26
c.
30
d.
32


Solution:

n - 5 > 26
[Original inequality.]

n - 5 + 5 > 26 + 5
[Add 5 to each side.]

n > 31
[Simplify.]

Among the choices, 32 is the only number that is a solution of the inequality n - 5 > 26.


Correct answer : (4)
 5.  
Which of the following choices is the solution for the inequality, 2x + 1 > 3?
a.
1
b.
-1
c.
2


Solution:

2x + 1 > 3
[Original inequality.]

2x + 1 - 1 > 3 - 1
[Subtract 1 from each side.]

2x > 2
[Simplify.]

2x2 > 22
[Divide each side by 2.]

x > 1
[Simplify.]

The solution greater than 1 from the choices is 2.


Correct answer : (4)
 6.  
Which of the following choices is a solution of the inequality, x - 5 4 > 3?
a.
4
b.
5
c.
2
d.
3


Solution:

A solution of the inequality is any value of the variable that makes the inequality true.

x - 54 > 3
[Original inequality.]

x - 54 + 54 > 3 + 54
[Add 5 / 4 to each side.]

x > 174
[Simplify.]

Among the choices, 5 is the only number that is a solution of the inequality x - 5 / 4 > 3.


Correct answer : (2)
 7.  
Which of the following choices is the solution for the inequality, x - 3 4 < 2?
a.
4
b.
2
c.
5
d.
3


Solution:

x - 34 < 2
[Original inequality.]

x - 34 + 34 < 2 + 34
[Add 3 / 4 to each side.]

x < 114
[Simplify.]

x < 2.7
[express the fraction as decimal.]

Among the choices, 2 is the only number that is solution for the inequatiy x - 3 / 4< 2.


Correct answer : (2)
 8.  
Which of the following choices is the solution of the inequality, x + 1 4 < 12?
a.
13
b.
14
c.
11
d.
12


Solution:

A solution of the inequality is any value of the variable that makes the inequality true.

x + 14 < 12
[Original inequality.]

x + 14 - 14 < 12 - 14
[Subtract 1 / 4 from each side.]

x < 474
[Simplify.]

Among the choices, 11 is the only number that is a solution of the inequality x + 1 / 4 < 12 .


Correct answer : (3)
 9.  
Solve the inequality.
x + 4 5 > 8
a.
x < 36 5
b.
x > 36 5
c.
x36 5
d.
x36 5


Solution:

x + 45 > 8
[Original inequality.]

x + 45 - 45 > 8 - 45
[Subtract 4 / 5 from each side.]

x > 365
[Simplify.]


Correct answer : (2)
 10.  
Solve the inequality.
n - 4 5 < 3 4
a.
n < 31 20
b.
n31 20
c.
n31 20
d.
n > 31 20


Solution:

n - 45 < 34
[Original inequality.]

n - 45 + 45 < 34 + 45
[Add 4 / 5 to each side.]

n < 15+1620
[Simplify.]

n < 3120
[Simplify.]


Correct answer : (1)

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