College Algebra: Section 1.1a (Packet #1)
By the end of the section, you should be able to:
- Identify and give an example of numbers contained in each subset of the Real Numbers.
- Solve inequalities and compound inequalities. (review from Alg. 2 Section 1.5)
- Use set-builder notation to identify sets of numbers and solutions of inequalities.
- Use interval notation to describe solutions of inequalities
- Solve absolute value equations and inequalities. (review from Alg. 2 Section 1.6)
Definitions:
- Set: A collection/group of “things” (objects, numbers, etc.)
- Element: A specific/distinct “thing” (object, number, etc.) in a set.
- Inequality: a relationship between two expressions when one expression is greater than (>), greater than or equal to (≥), less than (<), or less than or equal to (≤) the other expression.
- Absolute Value: the distance a real number x is away from zero.
- Extraneous Solution: a solution found from an original equation that is not a solution to the original equation
Subsets of Real Numbers
🎥 Example 1
🎥 Example 1
Properties of Inequalities
**For a more extensive review of Inequalities, please see Algebra 2 Section 1.5
**For a more extensive review of Inequalities, please see Algebra 2 Section 1.5
**The two symbols < and > are called strict inequality signs, while the symbols ≤ and ≥ are nonstrict inequality signs.
Example: a < b can be read as: “a is strictly less than b” meaning that a will never be equal/the same as b, it will always be less than b.
Set - Builder Notation
The following notation is known as set-builder notation. It is used to describe sets of numbers with specific properties.
The following notation is known as set-builder notation. It is used to describe sets of numbers with specific properties.
Examples of Absolute Value Properties
🎥 Examples 3-6
🎥 Examples 3-6
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