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Polynomial Inequalities
RationalInequalities
Systems of
Inequalities
DescribingGraphs
Absolute Value
Inequalities
Interval Notation
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ApplyingInequalities
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Solve x2<-x+6
-3<x<2
Solve x2 + 2 ≥ 3x
x ≤ 1 or x ≥ 2
Solve x3<x
x < -1 or 0 < x < 1
Solve
0)2()1(
xx
x < -2 or x > 1
What is a rational function?
A function of the form
where and are polynomials.
Solve
0)3()9( 2
xx
x<-3 or -3<x<3or
x<3 and x≠-3
Graph the solution to the Graph the solution to the system of inequalities:system of inequalities:
y ≥ -x + 1y ≥ -x + 1
y ≥ xy ≥ x
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
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
Describe the following Describe the following graph with an inequality.graph with an inequality.
y≤-x+10
Describe the following graph Describe the following graph with a system of inequalities.with a system of inequalities.
⅓x – 3 ≤ y ≤ ⅓x + 3
Describe the following graph with Describe the following graph with a system of inequalitiesa system of inequalities..
0 ≤ y ≤ 2x
x < 3
Solve | 2x + 3 | < 6
-4.5 < x < 1.5
Solve | 5x | > 15
x < -3 or x > 3
Solve | x + 12 | + 3 > 17
X < -26 or x > 2
Graph [-9, -5) U (0, ∞) Graph [-9, -5) U (0, ∞) on a number line on a number line
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.
(-4, 2)U(7, ∞)
Solve xSolve x3 3 > 2x. Write the > 2x. Write the solution in interval solution in interval
notation. notation.
(- ,0) U ( ,∞)(- ,0) U ( ,∞)2 2
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.
x > 2
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?
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.
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.
0.5 ≤ t ≤ 3.5
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