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## Inequalities and Applications■ Solving Inequalities ■ Interval Notation ■ The Addition Principle for Inequalities ■ The Multiplication Principle for Inequalities ■ Using the Principles Together ■ Problem Solving
Solving Inequalities A _______ is any value for a variable that makes an inequality ____ . The set of all solutions is called the . Examples
•_________________________ •_________________________ the end points from the set Interval Notation •_________________________ the end points from the set. If a and b are real numbers such that a < b: The open interval (a, b) is the set of all x’s graphed The closed interval [a, b] is the set of all x’s graphed The half-open interval (a, b] is the set of all x’s graphed The interval [a, ∞ ) is the set of all x’s graphed The interval (-∞, a) is the set of all x’s graphed
1. (-2, 4] Write each in set notation: 1. (-2, 4] Write each in interval notation: 1. {x | 1 < x < 7}
For any real numbers a, b, and c:
Solve and graph, also write solution in set and interval notation.
Plan A: $300 plus $9 per hour or Plan B: Straight $12.50 per hour. If the job takes n hours, what is the value of n so that Plan B is better for Tom.
■ Intersection of Sets and Conjunctions of ■ Unions of Sets and Disjunctions of Sentences ■ Interval Notation and Domains
A and B is the set of all elements that are common to both A and B. Intersection is written as ______ A _______________is two or more sentences are joined by _________. Ex: a conjunction of inequalities
Note that for a < b,
is the combination of all elements contained in both A and/or B. Union is written as _________ A is two or more sentences are joined by _______. Ex: a disjunction of inequalities
Example Solve and graph: |