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WU # 13
1
2
3
4
5
9y +1 < 19
5y +2 -y > 8
-7y -14
4y – 7y -7 < y + 9
-5y + 6 21
y < 2
y - 3
y > -4
y 2
2
3y
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 ÷)
< > “is less than”
“is less than or
equal to”
“is greater than”
“is at least”
“is at most”
“is more than”
“is more than or
equal to”
Note card
“x” is 2
x = 2
-2-6 -4 0 642
“x” is at least 2
x 2
“x” is 2
x = 2
-2-6 -4 0 642
“x” is at least 2
x 2
“x” is at most 2
x 2
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
< 20 12+ 2n < 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) <
753x + 3 < 75
x < 2424, 25, 26
23, 24, 25
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
18, 19, 20
x < 18.67
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
x + (3 + 2x) < 42 3x + 3 <
42x < 1312
the “first” integer is 3 + 2x
27 13,29 ?
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
2w + 2(5 + 2w) > 28 6w + 10 >
28w > 3
length is 5 + 2w
The base of a triangle is 8 cm. What height will make the area greater than 32 cm2?
Let h = the height
4h > 32
h > 8
Area = ½ • b • h ½ • 8 • h
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
64 + 0.2s 200
Pay = 64 + 0.20(s)
0.2s 136s 680
5 • • 5
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