Solve each rational inequality by hand. (3-2 x)/(1+x)<0 |...

Name: Problem 59, Chapter 5: A Graphical Approach to Precalculus with Limits
Uploaded: 2020-08-18T22:11:34-08:00
Duration: 1 min 54 s
Channel: Amy Jiang
Description: Solve each rational inequality by hand. (3-2 x)/(1+x)<0

Key Concepts

Domain Restrictions

Domain restrictions refer to the values that are not allowed because they make the denominator zero or result in undefined expressions, such as taking the square root of a negative number (if applicable). In the context of rational inequalities, these restrictions must be considered to ensure that the solution set only includes values where the expression is defined.

Rational Inequalities

A rational inequality involves an inequality between two expressions that are ratios of polynomials. Solving these problems typically involves finding where the rational expression is positive or negative by analyzing the signs of the numerator and denominator across its domain.

Critical Points

Critical points are the values of the variable that make either the numerator or the denominator zero. These points are important because they are potential boundaries where the sign of the rational expression may change, and values making the denominator zero are excluded from the solution since the expression is undefined there.

Sign Chart Analysis

Sign chart analysis is a systematic method used to determine the sign of a rational expression across different intervals. After identifying the critical points, the number line is divided into intervals, and a test value from each interval is used to determine whether the expression is positive or negative in that interval.

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