Section 1.7 Linear Inequalities and Absolute Value Inequalities

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Section 1.7Linear InequalitiesandAbsolute
Value Inequalities
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• Interval Notation

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Example
Express the interval in set builder notation and
graph
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• Intersections and
• Unions of Intervals

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Example
Find the set
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Example
Find the set
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• Solving Linear Inequalities
• in One Variable

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Example
Solve and graph the solution set on a number line
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Checking the solution of a linear inequality on
a Graphing Calculator
Separate the inequality into two equations.
The intersection of the two lines is at (1,3).
You can see this because both y values are the
same, 3. The region in the red box is where
the values of y1 is greater than y2.
The region on the graph of the red box is where
y1 is greater than y2. This is when x is greater
than 1.
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• Inequalities with
• Unusual Solution Sets

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Example
Solve each inequality
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• Solving
• Compound Inequalities

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Example
Solve and graph the solution set on a number line.
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• Solving Inequalities
• with Absolute Value

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Example
Solve and graph the solution set on a number line.
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Example
Solve and graph the solution set on a number line.
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• Applications

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Example
A national car rental company charges a flat rate
of 320 per week for the rental of a 4 passenger
sedan. The same car can be rented from a local
car rental company which charges 180 plus .20
per mile. How many miles must be driven in a
week to make the rental cost for the national
company a better deal than the local company?
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Solve the absolute value inequality.
(a) (b) (c) (d)
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Solve the linear inequality.
(a) (b) (c) (d)