Skip to main content
Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblema 71
Capitolo 2, Problema 71

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 2|4 - (5/2)x| + 6 = 18

Guida verificata passo dopo passo
1
Start by isolating the absolute value expression. Subtract 6 from both sides of the equation: 2\(\left\)|4 - \(\frac{5}{2}\)x\(\right\)| + 6 - 6 = 18 - 6, which simplifies to 2\(\left\)|4 - \(\frac{5}{2}\)x\(\right\)| = 12.
Next, divide both sides of the equation by 2 to further isolate the absolute value: \(\frac{2\left|4 - \frac{5}{2}\)x\(\right\)|}{2} = \(\frac{12}{2}\), giving \(\left\)|4 - \(\frac{5}{2}\)x\(\right\)| = 6.
Recall that if \(\left\)|A\(\right\)| = B, where B > 0, then A = B or A = -B. Apply this property to get two separate equations: 4 - \(\frac{5}{2}\)x = 6 and 4 - \(\frac{5}{2}\)x = -6.
Solve each equation for x separately. For the first equation, subtract 4 from both sides and then multiply both sides by the reciprocal of \(\frac{5}{2}\) to isolate x. Repeat the process for the second equation.
Check your solutions by substituting them back into the original equation to ensure they satisfy the 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:
3m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Absolute Value Equations

An absolute value equation involves expressions within absolute value bars, which represent the distance from zero on the number line. To solve such equations, set the expression inside the absolute value equal to both the positive and negative values of the number on the other side of the equation.
Video consigliato:
06:00
Categorizing Linear Equations

Isolating the Absolute Value Expression

Before solving an absolute value equation, isolate the absolute value expression on one side of the equation. This often involves performing inverse operations like subtraction or division to simplify the equation and prepare it for splitting into two cases.
Video consigliato:
05:09
Introduction to Algebraic Expressions

Solving Linear Equations

After splitting the absolute value equation into two linear equations, solve each one by applying algebraic techniques such as distributing, combining like terms, and isolating the variable. Check each solution in the original equation to verify its validity.
Video consigliato:
04:02
Solving Linear Equations with Fractions
Pratica correlata
Domanda del libro di testo

Without solving the given quadratic equation, determine the number and type of solutions. 9x2=2−3x9x^2 = 2-3x

1034
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. 5x + 9 = 9(x + 1) - 4x

971
views
Domanda del libro di testo

Find all values of x such that y = 0. y = 1/(5x + 5) - 3/(x + 1) + 7/5

782
views
Domanda del libro di testo

In Exercises 59–94, solve each absolute value inequality. |x - 1| ≥ 2

772
views
Domanda del libro di testo

Evaluate x2 - 2x + 2 for x = 1 + i.

960
views
Domanda del libro di testo

Solve each equation in Exercises 65–74 using the quadratic formula. 4x2=2x+74x^2 = 2x + 7

903
views