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Soving Equations with Inequality

See the attached file.

Solve using the addition and Multiplication principle;

1. 9x-6<-33

2. A car rents for $50 per day plus 20 cents per mile; You are on a daily budget of $88. What mileage will allow you to stay within your budget? The solution is {m l m < ? }

3. The formula R = - 0.075t + 3.85 can be used to predict the worlds record in the 1500 meter run, t years after 1930. Determine an inequality that identifies the years in which the world record will be less than 3.7 minutes. Solve for t.
t > ? round to the nearest whole number.

4. A certain kind of animal weighs about 75 pounds at birth and gains about 2 pounds per day for the first few weeks. Determine those days for which the animal weight is more than 125 pounds.
The animals weight is more than 125 pounds when the animal is more than ? days old

5. Joe's Electric made 16 customers calls last week and 24 calls this week. How many calls must be made next week in order to maintain an average of at least 20 calls for the three week period?
At least ? calls must be made to maintain an average of 20 calls.

6. A metal stays solid Fahrenheit temperature below 1585.9° (Determine in terms of an inequality) those Celsius temperatures for which the metal stays solid. Use the formula F = 9/5*(C)+32

The solution set is {ClC < ? °}.

Attachments

Solution Preview

Please refer attached file for better clarity of expressions. Some of the characters are missing here.

Solution:

1. 9x-6<-33

Adding 6 both sides, we get
9x-6+6<-33+6
9x<-27
Multiplying both sides by 1/9 we get
9x*1/9<-27*1/9
x<-3

2. A car rents for $50 per day plus 20 cents per mile; You are on a daily budget of $88. What mileage will allow you to stay within your budget?

Let m be the mileage, total cost=50+0.2*m=50+0.2m
Budget is $88
So, 50+0.2m 88
Adding -50 both sides we get
50+0.2m-50 88-50
0.2m 38
Multiplying by (1/0.2=5) both sides, we get
5*0.2m 38*5
m 190
The solution is {m l m < 190 }

3. The formula R = - 0.075t + 3.85 can be used to predict the worlds record in the 1500 ...

Solution Summary

There are 6 word problems. Solutions to these problems explain the methodology to convert word problems into equations with inequality and solve them.

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