4-5 Using InequalitiesWarm-up Problems• Solve.1.

2.

3.

4.

9 1 19u

5 2 8b b

7 14c

4 7 2 5x x x

Chapter 44-5 Using Inequalities

• Translate to an inequality.• A number y is greater than 4.

• A number x is less than or equal to 2.5

• A number m is at least 3.

• A number p is at most .

• 3 is greater than or equal to some number n.

• 12 more than twice a number is less than 20.

Example 1

y 4

x 2 5.

m 3

p 13

3 n

2 12 20x

13

• Translate to an inequality.a. A number x is greater than or equal to 8.

b. A number t is less than 12.

c. A number is at most 4.5

d. A number n is at least 0.

e. 3 less than a number is greater than 4.

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• Ruth Anne wants to enter her newborn calf in the 4-H competition at the county fair. In order to qualify for the competition, her calf must weigh at least 200 pounds. Calves weigh approximately 75 pounds at birth and gain 2 pounds per day for the first few weeks. How many days will it take before the calf’s weight exceeds 200 pounds?

• Question: How many days until the calf weighs 200 pounds?

• Data: Calf weighs 75 lb at birth; gains 2 lbs per day.

Example 2

• Let d = the number of days until the calf exceeds 200 pounds.

• 2d = the amount of weight gained in d days.

75 + 2d > 200 –75 –75

2d > 125 d > 62.5

• The medium-size box of dog food weighs 1 lb more than the small size. The large size weighs 2 lb more than the small size. If the total weight of the three boxes is at most 30 lb, what is the most a small box could weigh?

• Question: What is the most the small box could weigh?

• Data: Medium box weighs 1 lb more than the small;large box weighs 2 lb more than the small;total weight of the three boxes is at most 30 lb.

Example 3

• Let s = the maximum weight of the small box.• s + 1 = the maximum weight of the medium

box.• s + 2 = the maximum weight of the large box.

s s s ( ) ( )1 2 30

3 3 30s

3 27s

s 9

f. Each student agreed to sell at least 50 seed packages for a school project. Yesterday one student sold 22 packages, and today this student sold 18. How many more packages does the student need to sell to reach the goal of 50 packages?

g. In an algebra course you must get a total of at least 360 points on four tests for a grade of A. You get 85, 89, and 92 on the first three tests. What score on the last test will give you an A?

h. The sum of two consecutive integers is less than 35. What is the greatest possible pair?

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