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
5:07 minutes
Problem 42b
Textbook Question
Textbook QuestionSolve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^3≤4x^2
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
5mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Inequalities
Polynomial inequalities involve expressions where a polynomial is compared to a value using inequality symbols (e.g., ≤, ≥, <, >). To solve these inequalities, one typically finds the roots of the corresponding polynomial equation and tests intervals between these roots to determine where the inequality holds true.
Recommended video:
06:07
Linear Inequalities
Interval Notation
Interval notation is a mathematical notation used to represent a range of values on the real number line. It uses parentheses and brackets to indicate whether endpoints are included (closed interval) or excluded (open interval). For example, the interval [a, b) includes 'a' but not 'b', while (a, b) excludes both endpoints.
Recommended video:
05:18
Interval Notation
Graphing Solutions on a Number Line
Graphing solutions on a number line visually represents the solution set of an inequality. Each solution is marked with a dot or a line segment, depending on whether the endpoints are included or excluded. This graphical representation helps in understanding the range of values that satisfy the inequality.
Recommended video:
Guided course
02:35
Graphing Lines in Slope-Intercept Form
Related Videos
Related Practice