Domanda del libro di testo
Solve each equation in Exercises 83–108 by the method of your choice. 2x2 - x = 1
805
views
Ch. 1 - Equations and Inequalities
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 2, Problema 81
The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84.
Guida verificata passo dopo passo1
Recognize that the equation |x^2 - 6| = |5x| can be rewritten using the property that if |u| = |v|, then u = v or u = -v. Here, let u = x^2 - 6 and v = 5x.
Set up the two separate equations based on the property: 1) x^2 - 6 = 5x and 2) x^2 - 6 = -5x.
Solve the first equation x^2 - 6 = 5x by rearranging all terms to one side to form a quadratic equation: x^2 - 5x - 6 = 0.
Solve the second equation x^2 - 6 = -5x by rearranging all terms to one side to form another quadratic equation: x^2 + 5x - 6 = 0.
Use the quadratic formula or factoring method to find the roots of both quadratic equations, which will give the solutions to the original absolute value equation.
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:
4mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Absolute Value Definition and Properties
Absolute value represents the distance of a number from zero on the number line, always yielding a non-negative result. For any expressions u and v, the equation |u| = |v| means u = v or u = -v, reflecting that two values can have the same magnitude but opposite signs.
Video consigliato:
5:36
Change of Base Property
Solving Equations Involving Absolute Values
To solve equations with absolute values, rewrite the equation without absolute value bars by setting the inside expressions equal to each other and to their negatives. This creates two separate equations to solve, which together provide all possible solutions.
Video consigliato:
5:02Solving Logarithmic Equations
Quadratic Equations and Factoring
When solving equations like |x^2 - 6| = |5x|, the resulting equations often involve quadratics. Understanding how to rearrange, factor, or use the quadratic formula is essential to find all real solutions for x.
Video consigliato:
06:08Solving Quadratic Equations by Factoring
Pratica correlata
Domanda del libro di testo
In Exercises 59–94, solve each absolute value inequality. - 2|x - 4| ≥ - 4
1049
views
Domanda del libro di testo
In Exercises 77–92, use the graph to determine a. the function's domain; b.the x-intercepts, if any; and e. the missing function values, indicated by question marks, below each graph.
1153
views
Domanda del libro di testo
Solve each absolute value inequality. 5|2x + 1| - 3 ≥ 9
594
views
Domanda del libro di testo
Compute the discriminant. Then determine the number and type of solutions for the given equation. x2 - 3x - 7 = 0
909
views
Domanda del libro di testo
The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84.
642
views