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

College Algebra

1. Equations & Inequalities

Linear Inequalities

1:15 minutes

Problem 89b

Textbook Question

Solve each inequality in Exercises 86–91 using a graphing utility. (x - 4)/(x - 1) ≤ 0

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Inequalities

Inequalities express a relationship where one side is not necessarily equal to the other, using symbols like ≤, ≥, <, or >. In this case, the inequality (x - 4)/(x - 1) ≤ 0 indicates that we are looking for values of x that make the expression less than or equal to zero. Understanding how to manipulate and solve inequalities is crucial for finding the solution set.

Rational Functions

A rational function is a ratio of two polynomials, such as (x - 4)/(x - 1). Analyzing rational functions involves identifying their domain, asymptotes, and intercepts. For this inequality, we need to determine where the function is zero or undefined, which will help us understand the intervals to test for the inequality.

Graphing Utilities

Graphing utilities are tools that allow users to visualize mathematical functions and inequalities. By graphing the rational function (x - 4)/(x - 1), we can easily identify where the function is below or equal to zero. This visual representation aids in determining the solution set for the inequality by observing the regions of the graph that satisfy the condition.