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WU # 13 1 2 9y +1 < 19 y<2 5y +2 -y > 8 3 y 2 3 -7y -14 y2 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 x2 -6 -4 -2 0 2 4 6 “x” is 2 x=2 “x” is at least 2 “x” is at most 2 x2 -6 -4 x2 -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 t0 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