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
4:06 minutes
Problem 85c
Textbook Question
Textbook QuestionSolve each rational inequality. Give the solution set in interval notation. (2x-3)(3x+8)/(x-6)^3β₯0
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Inequalities
Rational inequalities involve expressions that are ratios of polynomials set against a comparison, such as greater than or equal to zero. To solve these inequalities, one must determine where the rational expression is positive or negative, which often requires finding critical points where the numerator or denominator equals zero.
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Rationalizing Denominators
Critical Points and Test Intervals
Critical points are values of the variable that make the numerator or denominator zero, leading to potential sign changes in the rational expression. After identifying these points, the number line is divided into intervals, and test points from each interval are used to determine whether the expression is positive or negative within those intervals.
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05:18
Interval Notation
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 (closed intervals) or excluded (open intervals). For example, the interval [a, b) includes 'a' but not 'b', which is essential for expressing solution sets of inequalities accurately.
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Interval Notation
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