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5.6b: Graphing Inequality

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Last updated about 2 years ago
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Today's Lesson: Graphing Inequalities (Day 2)
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A.REI.12
Inequality Word Problems
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Review of Systems of Equations
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A1.A.CED.A.3
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Tonight's HW

Watch "HW: Linear Inequalities Systems Video" Formative assignment

--> take notes in your Algebra I notebook!

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1.

Would you rather live in a world where it constantly snows or always rains?

Would you rather live in a world without music or a world without movies?

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2.

Write your responses directly on the screen.

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3.

Place each inequality symbol from the left column below into two categories. One to describe its graph's boundary line (dashed or solid) and one to describe its graph's shaded half-plane relative to the boundary line (above or below).

  • \geq

  • <

  • >

  • \leq

  • SOLID boundary line

  • DASHED boundary line

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4.

Use Your Vocabulary: Categorize each inequality based on the boundary line of its graph.

  • y < 3x

  • 2y - 3x ≤ 9

  • 4y ≥ x - 1

  • y > -5x + 4

  • Solid boundary line

  • Dashed boundary line

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5.

Of the 10 points added to the graph, which represent solutions of the inequality?

Select all that apply.

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6.

Graph the following inequality by drawing on the image. Remember to emphasize whether your line is dotted or solid, and which side of the line should be shaded.

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7.

What is the graph of the inequality below?

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8.

An electronics store sells DVD players and cordless telephones. The store makes a $75 profit on the sale of each DVD player (d) and a $30 profit on the sale of each cordless telephone (c). The store wants to make a profit of at least $255.00 from its sales of DVD players and cordless phones. Which inequality describes this situation?

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9.

Mary babysits for $4 per hour. She also works as a tutor for $7 per hour. She is only allowed to work 13 hours per week. She wants to make at least $65. Write and graph a system of inequalities to represent this situation.

Inequality Representing Hours:

Inequality Representing Money Earned:

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10.

You can work a total of no more then 41 hours each week at your two jobs. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn more than $254 each week to pay your bills. Write a system of inequalities that shows the various numbers of hours you can work at each job.

Inequality Representing Hours Worked:

Inequality Representing Money Earned:

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11.

Suppose you buy flour and cornmeal in bulk to make flour tortillas and corn tortillas. Flour costs $1.50 per pound and cornmeal costs $2.50 per pound. You want to spend less than $25 on flour and cornmeal, but you need at least 6 pounds altogether.

Let's write a system of linear inequalities to represent this situation.

Inequality Representing Pounds:

Inequality Representing Cost:

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12.

Review!

Solve the system by substitution.

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13.

Solve the system by elimination.