Transcript Linear Inequalities Lesson 2.4 Inequalities  Definition   Start with an equation 3x + 5 = 17 Replace the equals sign with one of   

Linear Inequalities
Lesson 2.4
Inequalities

Definition


Start with an equation 3x + 5 = 17
Replace the equals sign with one of
   

Examples
2x  5  7
8 x  2  3 x  6
Note that each of these can be changed into
the form ax + b § 0
where the § is the required inequality symbol
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Solving Inequality in One
Variable – Symbolic Method

Treat inequality in similar manner as an
equation




Add same thing to both sides of inequality
Multiply both sides by same positive value
If negative value used, inequality reverses
Try it!
Inequality
remains
same
<
3x  6  9
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Intersection of Graphs Method
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
Given f(x) > g(x)
Graph both f(x) and g(x)
Find the point of intersection
•
f(x)
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The solution set includes the
x-values where f(x) is above g(x)
g(x)
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Try It Out

Given


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x  2  10.5 13.7 x
Graph each side of the equation
Find intersection
Decide which side of the intersection matches
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X-Intercept Method
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Write the inequality as h(x) < 0
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Graph y = h(x)
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Solutions occur where graph is below x-axis
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Numerical Method
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Write the inequality as h(x) < 0
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Place h(x) in Y= screen

Use Tables (♦Y) and
observe values of x
where the function
is less than 0
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Assignment

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Lesson 2.4A
Page 142
Exercises 1 – 73 EOO
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Compound Inequality
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
Definition:
Two inequalities connected by the words and or
or
Examples
x  5 or
x  0 and
x  12
x7
3  1  x  2 x
Anything in this format should be considered
an "and" compound inequality
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Interval Notation

Solution displayed in interval notation [-1, 2)
[


)
The [ or ] means that the number is included in the
interval
The ( or ) means that the endpoint is not part of the
interval
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Solving Compound Inequality
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Symbolically
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Add the same thing to each part
Multiply each part by same positive number
Justify each step in the
sequence to the right
3  3 x  6  12
3  3 x  6
1  x  2
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Solving Compound Inequality
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Graphically


Graph all three parts
of the inequalities as
functions
The solution will
be the values of
x for which the
middle function is
between the other two
2x  5
0.2 x 
8
3
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Try It Out

Temp in Fahrenheit x miles
above ground level
given by T(x) = 85 – 19x

Use intersection of graphs to
determine when temp is < 32F
What does x-intercept on graph
y = T(x) represent?
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Linear Regression
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Home ownership rates given by table
x
P
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1900
47%
1950
55%
1980
64%
2006
69%
Determine a linear modeling function
Estimate years when ownership percent was
between 58% and 60%
Do we interpolate or extrapolate?
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Assignments
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

Lesson 2.4B
Page 144
Exercises 83 – 99 EOO
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