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