Domanda del libro di testo
Without solving the given quadratic equation, determine the number and type of solutions.
1034
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 73
In Exercises 59–94, solve each absolute value inequality. |3x - 8| > 7
Guida verificata passo dopo passo1
Recall that an absolute value inequality of the form \(|A| > B\) (where \(B > 0\)) can be rewritten as two separate inequalities: \(A > B\) or \(A < -B\).
Identify the expression inside the absolute value: here, \(A = 3x - 8\) and \(B = 7\).
Set up the two inequalities based on the rule: \(3x - 8 > 7\) or \(3x - 8 < -7\).
Solve each inequality separately:
For \(3x - 8 > 7\), add 8 to both sides to get \(3x > 15\), then divide both sides by 3 to find \(x > 5\).
For \(3x - 8 < -7\), add 8 to both sides to get \(3x < 1\), then divide both sides by 3 to find \(x < \frac{1}{3}\).
Combine the solutions to express the final answer: \(x < \frac{1}{3}\) or \(x > 5\).
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:
5mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Absolute Value Definition
The absolute value of a number represents its distance from zero on the number line, always as a non-negative value. For an expression |A|, it equals A if A is non-negative, and -A if A is negative. Understanding this helps in rewriting absolute value inequalities into equivalent compound inequalities.
Video consigliato:
08:07
Vertex Form
Solving Absolute Value Inequalities
An inequality involving absolute value, such as |A| > B, can be split into two separate inequalities: A > B or A < -B, when B is positive. This approach allows solving for the variable by considering both cases where the expression inside the absolute value is greater than B or less than -B.
Video consigliato:
06:07Linear Inequalities
Compound Inequalities and Solution Sets
After splitting the absolute value inequality, the solutions form a compound inequality, often expressed as a union of intervals. Understanding how to combine these intervals and represent the solution set on a number line is essential for interpreting and communicating the final answer.
Video consigliato:
06:07Linear Inequalities
Pratica correlata
Domanda del libro di testo
Solve each equation in Exercises 65–74 using the quadratic formula. x2 - 6x + 10 = 0
1032
views
Domanda del libro di testo
Evaluate (x2 + 19)/(2 - x) for x = 3i.
968
views
Domanda del libro di testo
In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x + 1| + 5 = 3
899
views
Domanda del libro di testo
In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4x + 7 = 7(x + 1) - 3x
1094
views
Domanda del libro di testo
Exercises 73–75 will help you prepare for the material covered in the next section. Multiply: (7 - 3x)(- 2 - 5x)
908
views