MATH Integrated Math III  - Unit 9: Linear Inequalities
For the first three problems, graph each linear inequality on graph paper. Compare your solution to the given graph. If the given graph is correct, state T (True). If it is not correct, state F (False) and describe the difference.

1) y > 5x + 2

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2) –2x – y > 0

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3) Graph the inequality shown below and compare to the given graph.

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For the next two problems, determine if the given system of inequalities is the correct system for the graph. If it is correct, write T (true), and if it is not, write F (false), and then explain why the graph is not correct.

4) Is the given system of inequalities the correct system for the graph? Explain, if not.

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5) Is the given system of inequalities the correct system for the graph? Explain, if not.

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For the next two problems, find the maximum and minimum values, if they exist, of each objective function for the given constraints. Graph each of the inequalities and use the feasible region in the objective function.

6)

State the maximum and minimum values if they exist.


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7) State the maximum and minimum values if they exist.

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Use the following scenario to solve the next three problems: The Snowy Mountain Ski plant makes two types of skis. A pair of down hill skis requires 6 hours to fabricate and 1 hour to finish. A pair of cross-country skis requires 4 hours to fabricate and 1 hour to finish. The fabricating department has 108 hours of labor available per day. The finishing department has 24 hours of labor available per day. The company makes a profit of $40 on each pair of down hill skis and a profit of $30 on each pair of cross-country skis.

8) Write a system of inequalities to represent the constraints. State the letter of the correct answer.

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9) Graph the feasible region on a piece of graph paper and then write the objective function for profit.

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10) Find the maximum profit for the given constraints.

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Review

For the remaining problems, state the answer or the letter of the answer, whichever is appropriate.

11) Write an equation for the given slope and passes through the given point. Express the equation in slope-intercept form.

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12) Solve for “y”.

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13) Solve for “x”.

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14) Solve for “x”.

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15) Evaluate.

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16) Simplify.

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17) Evaluate the function given below for the following values: (a) x = –2, (b) x = 8.

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18) Compose the given functions as directed.

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19) Solve by substitution.

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20) Solve by elimination.

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