Algebra

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Think of a situation that can be modeled with a linear inequality. This must be a situation where more than one possible solution is acceptable.

Describe your situation and why more than one solution is possible. Write an inequality to model the situation and solve this inequality. You will want to show your work when solving your inequality. Be sure to explain why you chose the inequality symbol you chose, paying careful attention to the difference between <. >, < and > . Explain in words what the graph of your solution set would look like; include a discussion about the type of circle used at the boundary point and about whether the graph is shaded to the left or right. To include the underline under an inequality sign, choose the underline function on the Discussion Board to create a < or > symbol.

An Example of the Assignment:

The other day, I went to the post office to mail a care package to my mother. The post office informed me the cost would be $2.00 for the box and $1.50 per pound to mail the item. I only walked into the post office with a $10.00 bill. What is the maximum weight of the package (assuming no sales tax for this example) I could mail?

In this case, more than one solution is possible as there are several weights for the package that would cost less than $10.00 to mail.

Let w=the weight of the package.

I could model this situation with the following inequality:

2+1.5w<10 To solve I will take the following steps:

-2 -2

1.5w<8

—- —

1.5 1.5

w<5.33

The maximum weight the package can be is 5.33 pounds.

I chose the < as the package could weigh less than or equal to 5.33 pounds. If it was exactly 5.33 pounds, I would spend all $10.00 but still have enough money to mail the package. Any weight less than 5.33 pounds is also a possible solution as I would have enough money to mail the package.

The graph of this solution would have a closed circle at 5.33 (between 5 and 6) and an arrow that extends to the left on the number line.

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algebra

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