Domanda del libro di testo
Solve each equation in Exercises 41–60 by making an appropriate substitution.
593
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 51
In Exercises 51–58, solve each compound inequality. 6 < x + 3 < 8
Guida verificata passo dopo passo1
Understand that the compound inequality 6 < x + 3 < 8 means that x + 3 is greater than 6 and less than 8 at the same time.
To isolate x in the middle, subtract 3 from all three parts of the inequality: 6 - 3 < x + 3 - 3 < 8 - 3.
Simplify each part: 3 < x < 5.
Interpret the solution: x is any number greater than 3 and less than 5.
Express the solution in interval notation as (3, 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:
1mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Compound Inequalities
A compound inequality involves two inequalities joined together, often with 'and' or 'or'. In this case, the inequality 6 < x + 3 < 8 means x + 3 is greater than 6 and less than 8 simultaneously. Solving compound inequalities requires working on both parts at the same time.
Video consigliato:
06:07
Linear Inequalities
Solving Linear Inequalities
Solving linear inequalities involves isolating the variable on one side by performing inverse operations such as addition, subtraction, multiplication, or division. When solving 6 < x + 3 < 8, subtract 3 from all parts to maintain the inequality and find the range of x.
Video consigliato:
06:07Linear Inequalities
Properties of Inequalities
Properties of inequalities dictate how inequalities behave under operations. For example, adding or subtracting the same number from all parts of an inequality does not change its direction. Multiplying or dividing by a positive number also preserves the inequality, which is essential when manipulating compound inequalities.
Video consigliato:
06:07Linear Inequalities
Pratica correlata
Domanda del libro di testo
In Exercises 37–52, perform the indicated operations and write the result in standard form. (3√-5)(- 4√-12)
174
views
Domanda del libro di testo
Solve each equation in Exercises 47–64 by completing the square.
965
views
Domanda del libro di testo
Write each English sentence as an equation in two variables. Then graph the equation. The y-value is two more than the square of the x-value.
126
views
Domanda del libro di testo
Write each English sentence as an equation in two variables. Then graph the equation. y = 5 (Let x = -3, - 2, - 1, 0, 1, 2, and 3.)
976
views
Domanda del libro di testo
Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(x + 4) - 7 = - 4/(x + 4)
774
views