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Name: ___________________________
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Directions: Graph the following linear inequalities.
1. y ≤ 1/2 x – 4
Graphing Linear Inequalities and Absolute Value
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2. y > – 2 x – 4
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3. 2 x – 4 y < 6
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4. y = |x – 2|
Directions: Graph the following absolute value equations.
5. y = 2 |x|
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6. y = |2x|
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7. y = |2x – 1|
Directions: Answer the following questions and make sure to show all your work.
8. Use the graph below to answer questions (a – c).
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a. Write the equation of the inequality.
b. Is (2, 0) a solution of the inequality? Why or why not?
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c. Is (4, -2) a solution of the inequality? Why or why not?
9. A swim coach has at most $800 to buy equipment for the swim team. Eachpull buoy costs $5.50 and each kickboard costs $10. Let x represent the number of pull buoys and y represent the number of kickboards.
a. Write an inequality for the scenario. .
b. Graph the inequality.
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c. Could the coach purchase zeros pull buoys and 50 kick boards? Use yourgraph to explain your answer.
d. Could the coach purchase 125 pull buoys and 25 kickboards? Use your graph toexplain your answer.
e. Using your graph, identify one more combination of pull buoys and kickboards that work for your inequality. How do you know your combinationworks? Explain your answer.
10. You want to spend less than $100 at the store. You choose a combinationof shirts for $8.00 and shorts for $12. Let x equal the number of shirts youpurchase and y equal the number of shorts you purchase.
a. Write an inequality for the scenario. .
b. Graph the inequality.
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c. Can you purchase 2 shirts and 4 shorts? Use your graph to explain your answer.
d. Can you purchase 14 shirts and no shorts? Use your graph to explain your answer.
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e. Using your graph, identify one more combination of shirts and shorts thatwill work for your inequality. How do you know that your combination works?Explain your answer.
