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Two-Variable Inequalities
1. Solve problem 68 on page 539 of Elementary and Intermediate Algebra, and make sure to study the given graph. For the purposes of the assignment, it would be helpful to copy the graph onto your own scratch paper.
Problem 68. Shipping restrictions. The accompanying graph shows all of the possibilities for the number of refrigerators and the number of TVs that will fit into an 18-wheeler.
a) Write an inequality to describe this region.
b) Will the truck hold 71 refrigerators and 118 TVs?
c) Will the truck hold 51 refrigerators and 176 TVs?
Write a two- to three-page paper (not including the title page) that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example, and be concise in your reasoning. In the body of your essay, do the following:
Demonstrate your solution to all three portions of the above problem, making sure to include all mathematical work, and an explanation for each step.
Use the inequality you create from part (a) of problem 68 to evaluate the following two scenarios:
The Burbank Buy More store is going to make an order which will include, at most, 60 refrigerators. What is the maximum number of TVs that could also be delivered on the same 18-wheeler? Be sure to show all your work and how you came to that conclusion.
The next day, the Burbank Buy More decides they will have a television sale so they change their order to include at least 200 TVs. What is the maximum number of refrigerators that could also be delivered in the same truck? Be sure to show your work and how you came to that conclusion.
Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):
Solid line
Dashed line
Parallel
Linear inequality
Test point
2. ON SEPARATE SHEET
Demonstrating your understanding of compound inequalities and the effect that dividing by a negative has on an inequality. Read the following instructions in order and view the example to complete this PROBLEMS:
Your “and” compound inequality is
-9 < -1 + 4x < 15
Your “or” compound inequality is
8 – x > 15 or 6x – 13 > 11
Solve the compound inequalities as demonstrated in Elementary and Intermediate Algebra and the Instructor Guidance in the left navigation toolbar, being careful of how a negative x-term is handled in the solving process. Show all math work arriving at the solutions.
Show the solution sets written algebraically and as a union or intersection of intervals. Describe in words what the solution sets mean, and then display a simple line graph for each solution set as demonstrated in the Instructor Guidance in the left navigation toolbar.
Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):
Compound inequalities
And
Or
Intersection
Union
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