MRY Ch 4.4: Linear Inequalities Lesson & Practice (36 pts)

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Problem 1 Got It?

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Hint: There are 3 lines to consider:
y>x+10, y<x+10, and y=x+10.

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Problem 2 Got It? What is the graph of the inequality below?

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Problem 3 Got It? What is the graph of the inequality?

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Problem 3 Got It? What is the graph of the inequality?

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Answer to question to the left is

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Is (-1, 4) a solution of the inequality? Explain.

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Graph the linear inequality
As always, include important graph detail: label the axes, indicate axis scale by labeling at least one value on each axis, add arrows to the ends of lines, ensure that your line is appropriately dashed or solid, and shade one side of the boundary line, as appropriate.

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What is an inequality that represents the graph shown?

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Writing: To graph the inequality below, do you shade above or below the boundary line? Explain.

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To graph the inequality below, what type of boundary line do you use?

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To graph the inequality below, what type of boundary line do you use?

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Problem 4 Got It? For a party, you can spend no more than $12 on nuts. Peanuts cost $2/lb. Cashews cost $4/lb. What are three possible combinations of peanuts and cashews you can buy. Graph the inequality.
step 1: Let peanuts be x and cashews be y. Write an inequality.
step 2: Graph the inequality. (solve for y first to put in y=mx+b form)
step 3: choose any 3 points that are solutions (in the shaded area or on a solid line)
Note: In the video above any 3 points in the shaded area or on the line could be solutions. One of his circled points is actually (10,15) but (10,10) would also be a solution because it is in the shaded area.

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Solve It! You are buying paperback and hardcover books at a book sale. You must spend less than $20. Let x represent the paperbacks and y represent the hardcovers. Write an inequality to represent the situation. Do not include the $ sign in your inequality.

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Review: What compound inequality represents the phrase "all real numbers that are greater than 2 and less than or equal to 7"?

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Vocabulary Review A solution is a value or values which, when substituted for a variable, make an equation true. Determine the solution of each inequality below.

Solution: x > 20
Solution: x < 20
Solution: m > 6
Solution: m < 6

x + 17 < 37
2m + 3 > 15

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Use Your Vocabulary: Identify the linear inequality in two variables.

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Problem 1 Got It?

Hint: There are 3 lines to consider:y>x+10, y<x+10, and y=x+10.

Problem 2 Got It? What is the graph of the inequality below?

Problem 3 Got It? What is the graph of the inequality?

Problem 3 Got It? What is the graph of the inequality?

Answer to question to the left is

Is (-1, 4) a solution of the inequality? Explain.

Graph the linear inequality As always, include important graph detail: label the axes, indicate axis scale by labeling at least one value on each axis, add arrows to the ends of lines, ensure that your line is appropriately dashed or solid, and shade one side of the boundary line, as appropriate.

What is an inequality that represents the graph shown?

Writing: To graph the inequality below, do you shade above or below the boundary line? Explain.

To graph the inequality below, what type of boundary line do you use?

To graph the inequality below, what type of boundary line do you use?

Solve It! You are buying paperback and hardcover books at a book sale. You must spend less than $20. Let x represent the paperbacks and y represent the hardcovers. Write an inequality to represent the situation. Do not include the $ sign in your inequality.

Review: What compound inequality represents the phrase "all real numbers that are greater than 2 and less than or equal to 7"?

Vocabulary Review A solution is a value or values which, when substituted for a variable, make an equation true. Determine the solution of each inequality below.

Use Your Vocabulary: Identify the linear inequality in two variables.

Reflection: Math Success

Hint: There are 3 lines to consider:
y>x+10, y<x+10, and y=x+10.

Graph the linear inequality
As always, include important graph detail: label the axes, indicate axis scale by labeling at least one value on each axis, add arrows to the ends of lines, ensure that your line is appropriately dashed or solid, and shade one side of the boundary line, as appropriate.