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 61a
Capitolo 2, Problema 61a

Find all values of x satisfying the given conditions. y1 = 5(2x - 8) - 2, y2 = 5(x - 3) + 3, and y1 = y2.

Guida verificata passo dopo passo
1
Start by setting the two equations for y1 and y2 equal to each other, since y1 = y2. This gives the equation: 5(2x - 8) - 2 = 5(x - 3) + 3.
Distribute the 5 on both sides of the equation. For the left-hand side, distribute 5 to (2x - 8), and for the right-hand side, distribute 5 to (x - 3). This results in: 10x - 40 - 2 = 5x - 15 + 3.
Simplify both sides of the equation by combining like terms. On the left-hand side, combine -40 and -2 to get -42. On the right-hand side, combine -15 and 3 to get -12. The equation now becomes: 10x - 42 = 5x - 12.
Isolate the variable x by first eliminating the 5x term from the right-hand side. Subtract 5x from both sides: 10x - 5x - 42 = -12. This simplifies to: 5x - 42 = -12.
Solve for x by adding 42 to both sides to isolate the term with x: 5x = 30. Then divide both sides by 5 to solve for x: x = 6.

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.

Linear Equations

Linear equations are mathematical statements that express the equality of two linear expressions. They can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. Understanding how to manipulate and solve these equations is crucial for finding the values of x that satisfy the given conditions.
Video consigliato:
06:00
Categorizing Linear Equations

Substitution Method

The substitution method involves replacing one variable with an equivalent expression from another equation. In this context, setting y1 equal to y2 allows us to create a single equation in terms of x. This method simplifies the problem and makes it easier to solve for the unknown variable.
Video consigliato:
04:03
Choosing a Method to Solve Quadratics

Solving for x

Solving for x involves isolating the variable on one side of the equation to find its value. This process may include combining like terms, applying inverse operations, and simplifying expressions. Mastery of this concept is essential for determining the specific values of x that satisfy the equality of the two linear equations.
Video consigliato:
5:02
Solving Logarithmic Equations
Pratica correlata
Domanda del libro di testo

Write each complex number in standard form. (1 - i)3

126
views
Domanda del libro di testo

In Exercises 61–64, write each complex number in standard form. (1 + i)3

786
views
Domanda del libro di testo

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x| = 8

650
views
Domanda del libro di testo

Solve each equation in Exercises 47–64 by completing the square. 4x2−4x−1=04x^2 - 4x - 1 = 0

819
views
Domanda del libro di testo

In Exercises 59–94, solve each absolute value inequality. |x + 3| ≤ 4

736
views
Domanda del libro di testo

In Exercises 61–66, find all values of x satisfying the given conditions. y1=x−35,y2=x−54,andy1−y2=1y_1 = \(\frac{x - 3}{5}\), \(\quad\) y_2 = \(\frac{x - 5}{4}\), \(\quad\) \(\text{and}\) \(\quad\) y_1 - y_2 = 1

882
views