WU # y +1 < 19 5y +2 -y > 8 -7y  -14 4y – 7y -7 < y y + 6  21 y < 2 y  - 3 y > -4 y  2

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 = “x” is at least 2 x  2

“x” is 2 x = “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 < n < 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 x < 24 24, 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 < 42 x < the “first” integer is 3 + 2x 2713,29 ?

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 > 28 w > 3 length is 5 + 2w

The base of a triangle is 8 cm. What height will make the area greater than 32 cm 2 ? 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 s  200 Pay = (s) 0.2s  136 s 

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