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En los problemas 35 a 58, resuelva la desigualdad no lineal. Escriba el conjunto solución usando notación de intervalos. Grafique el conjunto solución. $\frac{5}{x+8}<0$

   En los problemas 35 a 58, resuelva la desigualdad no lineal. Escriba el conjunto solución usando notación de intervalos. Grafique el conjunto solución.
$\frac{5}{x+8}<0$

Precálculo con avances de cálculo

Precálculo con avances de cálculo

Dennis G. Zill, José… 5th Edition

Chapter 1, Problem 47

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$\frac{5}{x+8}<0$ se puede reescribir como $5(x+8)>0$. Show more…

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En los problemas 35 a 58, resuelva la desigualdad no lineal. Escriba el conjunto solución usando notación de intervalos. Grafique el conjunto solución. $\frac{5}{x+8}<0$

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Key Concepts

Rational Inequalities

This concept involves solving inequalities where at least one expression is a fraction with a polynomial in the numerator and/or denominator. The general approach requires determining where the rational expression is positive, negative, or undefined, often by identifying critical points that divide the number line into intervals.

Domain Restrictions

When dealing with rational expressions, one must consider the values that make the denominator zero. These values are excluded from the solution set since division by zero is undefined. Recognizing and excluding these values is essential when solving rational inequalities.

Sign Chart Analysis

A sign chart or number line analysis is a method used to determine the sign of the rational expression in different intervals. By selecting test points in each interval created by the critical values, one can establish where the expression satisfies the inequality condition (e.g., less than zero) and thus obtain the correct solution set.

Interval Notation

Interval notation is a concise way to describe a set of numbers between two endpoints. It is commonly used to express solution sets for inequalities. It uses brackets and parentheses to indicate whether endpoints are included or excluded (with parentheses denoting exclusion, particularly important when the expression is undefined at a critical point).

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