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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

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4.5 Using Inequalities Goal: To translate phrases to mathematical inequalities and then solve

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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 ÷)

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< > “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

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“x” is 2 x = “x” is at least 2 x 2

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“x” is 2 x = “x” is at least 2 x 2 “x” is at most 2 x 2

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A number “y” is less than 4 y < 4 A number “y” is 3 less than 4 y = 4 - 3

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A number “r” is at most -6 r -6

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A number “t” is at least 0 t 0

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12 more than twice a number is less than 20 < n < 20

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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

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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

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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 ?

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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

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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

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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

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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

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Assignment: Page 189 (2-26) even Write the questions for 2-14 and just write the data for 16-26

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