Domanda del libro di testo
Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (4−2x)/(3x+4)≤0
458
views
Ch. 3 - Polynomial and Rational Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 4, Problema 50
Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (3x+5)/(6−2x)≥0
Guida verificata passo dopo passo1
Identify the rational inequality: \(\frac{3x+5}{6-2x} \geq 0\).
Find the critical points by setting the numerator and denominator equal to zero separately: solve \(3x + 5 = 0\) and \(6 - 2x = 0\).
Determine the values of \(x\) where the expression is undefined (denominator zero) and where the expression equals zero (numerator zero). These points divide the number line into intervals.
Test a value from each interval in the original inequality to determine if the expression is positive or negative in that interval.
Based on the test results, write the solution set including points where the expression equals zero (if inequality is \(\geq\)) and exclude points where the expression is undefined, then express the solution in interval notation.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
6mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Rational Inequalities
Rational inequalities involve expressions where one polynomial is divided by another, and the inequality compares this ratio to zero or another value. Solving them requires finding where the expression is positive, negative, or zero, considering the domain restrictions where the denominator is not zero.
Video consigliato:
3:21
Nonlinear Inequalities
Critical Points and Sign Analysis
Critical points are values that make the numerator or denominator zero, dividing the number line into intervals. By testing points in each interval, you determine the sign of the rational expression, which helps identify where the inequality holds true.
Video consigliato:
05:46Point-Slope Form
Interval Notation and Graphing Solutions
Interval notation concisely represents sets of real numbers satisfying the inequality, using parentheses for excluded endpoints and brackets for included ones. Graphing on a number line visually shows these intervals, aiding in understanding the solution set.
Video consigliato:
05:18Interval Notation
Pratica correlata
Domanda del libro di testo
Write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 2x2 but with the given point as the vertex. (5, 3)
1049
views
Domanda del libro di testo
In Exercises 49–50, find all the zeros of each polynomial function and write the polynomial as a product of linear factors. g(x) = x^4 - 6x^3 + x^2 + 24x + 16
732
views
Domanda del libro di testo
Use transformations of f(x)=1/x or f(x)=1/x2 to graph each rational function. g(x)=1/(x+2)2
945
views
Domanda del libro di testo
Write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 2x2 but with the given point as the vertex. (−10, −5)
1031
views
Domanda del libro di testo
In Exercises 49–50, find all the zeros of each polynomial function and write the polynomial as a product of linear factors.
606
views