1.7 Linear Inequalities and Compound Inequalities
Miller & Gerken, College Algebra 2e — Pages 168-179
Learning Objectives
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Solve linear inequalities
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Graph solution sets
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Solve compound inequalities with AND
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Solve compound inequalities with OR
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Express solutions in interval notation
Key Concepts
Inequality Properties
When multiplying or dividing by a negative number, flip the inequality sign.
Compound Inequalities
- AND (Intersection)
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Both conditions must be true.
\[a < x \text{ AND } x < b \Rightarrow a < x < b\]
- OR (Union)
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At least one condition must be true.
\[x < a \text{ OR } x > b\]
Three-Part Inequalities
\[a < x < b \quad \text{means} \quad a < x \text{ AND } x < b\]
Solve by isolating \(x\) in the middle, performing the same operation on all three parts.
Examples
Example 1. Example 1 (p. XX)
Work through textbook example…
Practice Problems
Problem 1 (p. XX, #YY)
Problem:
My Work:
Answer:
Section Summary
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Key point 1
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Key point 2
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Key point 3