Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
1. Equations & Inequalities
Linear Inequalities
2:30 minutes
Problem 31a
Textbook Question
Textbook QuestionSolve each inequality. Give the solution set in interval notation. | 1/2 - x | ≤ 2
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value Inequality
An absolute value inequality expresses a condition where the distance of a variable from a certain point is constrained. For example, |x - a| ≤ b means that x is within b units of a. To solve such inequalities, we typically break them into two separate inequalities, one for the positive case and one for the negative case.
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Interval Notation
Interval notation is a mathematical notation used to represent a range of values. It uses parentheses and brackets to indicate whether endpoints are included or excluded. For instance, (a, b) means all numbers between a and b, excluding a and b, while [a, b] includes both endpoints.
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Solving Inequalities
Solving inequalities involves finding the values of a variable that satisfy a given condition. This process often includes isolating the variable, manipulating the inequality, and considering the direction of the inequality sign, especially when multiplying or dividing by negative numbers. The solution is typically expressed in interval notation.
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