# 3. The sum of two integers is greater than 23. One integer is 5 less

```WU # 13
1
2
9y +1 < 19
y<2
5y +2 -y > 8
3
y 
2
3
-7y  -14
y2
4
4y – 7y -7 < y + 9
5
y > -4
-5y + 6  21
y-3
4.5 Using Inequalities
• Goal: To translate phrases to mathematical
inequalities and then solve
The small 2 letter word IS….
Is huge! It tells you it is either =, >, < , ≥, or≤
If there is not an “is” then it is strictly an
operation (+, -,X, or ÷)
Note card
<

>
“is less “is less than
“is
than” or equal to” greater
than”
“is at
“is more
most”
than”

“is at
least”
“is more
than or
equal to”
“x” is 2
x=2
“x” is at least 2
x2
-6
-4
-2
0
2
4
6
“x” is 2
x=2
“x” is at least 2
“x” is at most 2
x2
-6
-4
x2
-2
0
2
4
6
A number “y” is less than 4
y<4
A number “y” is 3 less than 4
y=4-3
A number “r” is at most -6
r  -6
A number “t” is at least 0
t0
12 more than twice a number is
less than 20
12+ 2n<<20
20
The sum of three consecutive
integers is less than 75. What
are the greatest possible
values of these integers?
Let x = the first consecutive integer
x + (x + 1) + (x + 2) < 75
3x + 3 < 75
24, 25, 26
23, 24, 25
x < 24
The sum of three consecutive integers
is less than 59. What are the greatest
possible values of these integers?
Let x = the first consecutive integer
x + (x + 1) + (x + 2) < 59
3x + 3 < 59
3x < 56
x < 18.67
18, 19, 20
2. Find the greatest possible pair
of integers such that one integer
is 3 more than twice the other
and their sum is less than 42.
Let x = the “other” integer
the “first” integer is 3 + 2x
x + (3 + 2x) < 42
12
27
13,29 ?
3x + 3 < 42
x < 13
The length of a rectangle is 5 cm
more than twice the width, and the
perimeter is greater than 28 cm.
What is the width of the rectangle?
Let w = the width
length is 5 + 2w
2w + 2(5 + 2w) > 28
6w + 10 > 28
w>3
The base of a triangle is 8 cm.
What height will make the area
greater than 32 cm2?
Let h = the height
Area = ½ • b • h  ½ • 8 • h
4h > 32
h>8
Gail works for a vending company. She
gets paid \$64 per week plus 20% of her
total sales. How much will her total
sales for the week have to be in order
for Gail to make at least \$200?
Let s = total sales
Pay = 64 + 0.20(s)
64 + 0.2s  200
5 • 0.2s  136 • 5
s  680
How long must the sides of an
equilateral triangle be in order for the
perimeter to be greater than 45 m?
Let s = each side
3s > 45
s > 15
Assignment:
Page 189
(2-26) even
Write the questions for 2-14 and
just write the data for 16-26
```
Prealgebra Terms