Linear Inequalities Lesson 2.4 Inequalities Definition Start with an equation 3x + 5 = 17 Replace the equals sign with one of
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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
2
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
3
Intersection of Graphs Method
Given f(x) > g(x)
Graph both f(x) and g(x)
Find the point of intersection
•
f(x)
The solution set includes the
x-values where f(x) is above g(x)
g(x)
4
Try It Out
Given
x 2 10.5 13.7 x
Graph each side of the equation
Find intersection
Decide which side of the intersection matches
5
X-Intercept Method
Write the inequality as h(x) < 0
Graph y = h(x)
Solutions occur where graph is below x-axis
6
Numerical Method
Write the inequality as h(x) < 0
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
Lesson 2.4A
Page 142
Exercises 1 – 73 EOO
8
Compound Inequality
Definition:
Two inequalities connected by the words and or
or
Examples
x 5 or
x 0 and
x 12
x7
3 1 x 2 x
Anything in this format should be considered
an "and" compound inequality
9
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
10
Solving Compound Inequality
Symbolically
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
11
Solving Compound Inequality
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
12
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 < 32F
What does x-intercept on graph
y = T(x) represent?
13
Linear Regression
Home ownership rates given by table
x
P
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
Lesson 2.4B
Page 144
Exercises 83 – 99 EOO
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