Writing Inequalities

1
Writing Inequalities
2
Translate the following sentences into
inequalities.
1) A number is greater than 16.2) A number
is less than 16.3) A number is at least 16.
4) A number is at most 16.
3
Translate the following sentences into
inequalities.
1) A number is greater than 16. N gt 162) A
number is less than 16.3) A number is at
least 16. 4) A number is at most 16.
4
Translate the following sentences into
inequalities.
1) A number is greater than 16. N gt 162) A
number is less than 16. N lt 163) A number is
at least 16. 4) A number is at most 16.
5
Translate the following sentences into
inequalities.
1) A number is greater than 16. N gt 162) A
number is less than 16. N lt 163) A number is
at least 16. N 164) A number is at most
16.
6
Translate the following sentences into
inequalities.
1) A number is greater than 16. N gt 162) A
number is less than 16. N lt 163) A number is
at least 16. N 164) A number is at most
16. N 16
7
Translate the following phrases into mathematical
expressions.
1) Three times a number decreased by four.2)
Five more than twice a number.3) The sum of
two consecutive integers.4) The sum of two
consecutive even integers.
8
Translate the following phrases into mathematical
expressions.
1) Three times a number decreased by four. 3N
- 42) Five more than twice a number.3) The
sum of two consecutive integers.4) The sum
of two consecutive even integers.
9
Translate the following phrases into mathematical
expressions.
1) Three times a number decreased by four. 3N
- 42) Five more than twice a number. 5
2N3) The sum of two consecutive integers.4)
The sum of two consecutive even integers.
10
Translate the following phrases into mathematical
expressions.
1) Three times a number decreased by four. 3N
- 42) Five more than twice a number. 5
2N3) The sum of two consecutive integers. N
N 14) The sum of two consecutive even
integers.
11
Translate the following phrases into mathematical
expressions.
1) Three times a number decreased by four. 3N
- 42) Five more than twice a number. 5
2N3) The sum of two consecutive integers. N
N 14) The sum of two consecutive even
integers. N N 2
12
For each of the following problems
1) Define a variable.2) Write an inequality.3)
Solve the inequality.
13
1) Three times a number increased by 8 is at
least 25. What is the number?
14
1) Three times a number increased by 8 is at
least 25. What is the number?
N the number
15
1) Three times a number increased by 8 is at
least 25. What is the number?
x 3
8

N the number
3N 8 25
16
1) Three times a number increased by 8 is at
least 25. What is the number?
x 3
8

N the number
3N 8 25N 5 2/3
17
2) Womens Sports Fitness Magazine states that
three times the weight of a backpack and its
contents should be less than your body weight to
avoid injury. How much weight can you put in
your backpack if your empty pack weighs 15 pounds
and if your weight is 120 pounds?
18
2) Womens Sports Fitness Magazine states that
three times the weight of a backpack and its
contents should be less than your body weight to
avoid injury. How much weight can you put in
your backpack if your empty pack weighs 15 pounds
and if your weight is 120 pounds?
W weight of contents
19
2) Womens Sports Fitness Magazine states that
three times the weight of a backpack and its
contents should be less than your body weight to
avoid injury. How much weight can you put in
your backpack if your empty pack weighs 15 pounds
and if your weight is 120 pounds?

x 3
(
lt
)
W weight of contents
3(W 15) lt 120
20
2) Womens Sports Fitness Magazine states that
three times the weight of a backpack and its
contents should be less than your body weight to
avoid injury. How much weight can you put in
your backpack if your empty pack weighs 15 pounds
and if your weight is 120 pounds?

x 3
(
lt
)
W weight of contents
3(W 15) lt 120W lt 25
21
3) The sum of two consecutive odd integers is
more than 136. Find the least pair of such
integers.
22
3) The sum of two consecutive odd integers is
more than 136. Find the least pair of such
integers.
i the first odd integeri 2 the second odd
integer
23
3) The sum of two consecutive odd integers is
more than 136. Find the least pair of such
integers.

gt
i the first odd integeri 2 the second odd
integeri i 2 gt 136
24
3) The sum of two consecutive odd integers is
more than 136. Find the least pair of such
integers.

gt
i the first odd integeri 2 the second odd
integeri i 2 gt 136i gt 67Therefore, the
integers must be 69 and 71.
25
4) The sum of two consecutive integers is at
least 35. Find the integers.
26
4) The sum of two consecutive integers is at
least 35. Find the integers.
i the first integeri 1 the next integer
27
4) The sum of two consecutive integers is at
least 35. Find the integers.


i the first integeri 1 the next integeri
i 1 35
28
4) The sum of two consecutive integers is at
least 35. Find the integers.


i the first integeri 1 the next integeri
i 1 35i 17Therefore, the integers are
17 and 18.