Solve each inequality. (x-3)/(x+2)<0

Name: Problem 41, Chapter 6: Intermediate Algebra
Uploaded: 2022-03-04T23:02:41-08:00
Duration: 42 s
Channel: Victor Salazar
Description: Solve each inequality. (x-3)/(x+2)<0

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Key Concepts

Rational Inequalities

Rational inequalities involve expressions that are ratios of two polynomials, and their solutions require determining where the entire expression is positive, negative, or zero. Solving these inequalities often involves considering both the behavior of the numerator and the denominator separately.

Critical Points

Critical points are the values where either the numerator or the denominator of a rational expression equals zero. These points partition the number line into distinct intervals, across which the sign of the expression can change. Identifying these points is essential for analyzing the behavior of the inequality.

Sign Analysis

Sign analysis is a method used to determine the sign of a rational expression over the intervals defined by the critical points. By selecting test points from each interval and substituting them into the expression, one can determine whether the expression is positive or negative in that interval.

Domain Restrictions

In solving rational inequalities, it is crucial to consider the domain of the expression, particularly where the denominator equals zero, as these values make the expression undefined. Excluding these values from the solution set ensures that only valid solutions are considered.

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