200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational...

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200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial nequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute Value Inequalities Interval Notation 100 200 300 Applying Inequalitie 100 200 300

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RationalInequalities

Systems of

Inequalities

DescribingGraphs

Absolute Value

Inequalities

Interval Notation

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Solve x2<-x+6

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-3<x<2

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Solve x2 + 2 ≥ 3x

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x ≤ 1 or x ≥ 2

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Solve x3<x

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x < -1 or 0 < x < 1

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Solve

0)2()1(

xx

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x < -2 or x > 1

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What is a rational function?

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A function of the form

where and are polynomials.

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Solve

0)3()9( 2

xx

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x<-3 or -3<x<3or

x<3 and x≠-3

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Graph the solution to the Graph the solution to the system of inequalities:system of inequalities:

y ≥ -x + 1y ≥ -x + 1

y ≥ xy ≥ x

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Graph the solution to the Graph the solution to the system of inequalities:system of inequalities:

2x - y ≤ 22x - y ≤ 2

2y + x < 22y + x < 2

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Graph the solution to the Graph the solution to the system of inequalities:system of inequalities:

y ≥ xy ≥ x22 – 2 – 2

x ≥ -3y + 6x ≥ -3y + 6

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Describe the following Describe the following graph with an inequality.graph with an inequality.

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y≤-x+10

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Describe the following graph Describe the following graph with a system of inequalities.with a system of inequalities.

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⅓x – 3 ≤ y ≤ ⅓x + 3

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Describe the following graph with Describe the following graph with a system of inequalitiesa system of inequalities..

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0 ≤ y ≤ 2x

x < 3

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Solve | 2x + 3 | < 6

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-4.5 < x < 1.5

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Solve | 5x | > 15

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x < -3 or x > 3

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Solve | x + 12 | + 3 > 17

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X < -26 or x > 2

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Graph [-9, -5) U (0, ∞) Graph [-9, -5) U (0, ∞) on a number line on a number line

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Solve Solve (x + 4)(x – 2)(x - 7)(x + 4)(x – 2)(x - 7) > 0. > 0.

Write the solution in Write the solution in interval notation. interval notation.

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(-4, 2)U(7, ∞)

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Solve xSolve x3 3 > 2x. Write the > 2x. Write the solution in interval solution in interval

notation. notation.

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(- ,0) U ( ,∞)(- ,0) U ( ,∞)2 2

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The profit a company earns as a function of items sold, x, is

represented by P(x)=x2+2x-8, write an inequality to describe how many

items need to be sold in order for the company to make a profit.

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x > 2

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Your new cell phone plan has a monthly access fee of $28.72 with a flat rate of $0.31 per minute.  If you want to keep your monthly bill under $40, how many minutes per month can you talk on your new cell

phone?

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Let x = number of minutes spent talking

$28.72 + .31x < 40.31x < 11.28

x < 36.38709677 You can use up to 36 minutes per month.

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The height of a rocket in feet is represented by the equation h(t)=-16t2+64t+72, where

t=time, in seconds. For what values of t will the rocket

remain at or above 100 feet from the ground.

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0.5 ≤ t ≤ 3.5


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