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 141
Capitolo 2, Problema 141

Solve: √(6x - 2) = √(2x + 3) - √(4x - 1).

Guida verificata passo dopo passo
1
Step 1: Start by isolating one of the square root terms. Add √(4x - 1) to both sides of the equation to get: √(6x - 2) + √(4x - 1) = √(2x + 3).
Step 2: To eliminate the square roots, square both sides of the equation. On the left-hand side, use the binomial expansion formula (a + b)^2 = a^2 + 2ab + b^2. This gives: (√(6x - 2))^2 + 2√(6x - 2)√(4x - 1) + (√(4x - 1))^2 = (√(2x + 3))^2.
Step 3: Simplify each term. The squares of the square roots simplify to their respective radicands: 6x - 2 + 2√((6x - 2)(4x - 1)) + 4x - 1 = 2x + 3.
Step 4: Combine like terms on the left-hand side. This results in: (6x - 2) + (4x - 1) + 2√((6x - 2)(4x - 1)) = 2x + 3. Simplify further to get: 10x - 3 + 2√((6x - 2)(4x - 1)) = 2x + 3.
Step 5: Isolate the remaining square root term by subtracting (10x - 3) from both sides: 2√((6x - 2)(4x - 1)) = 2x + 3 - (10x - 3). Simplify the right-hand side and proceed to square both sides again to eliminate the square root. Continue solving for x by simplifying and isolating x.

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:
9m

Concetti chiave

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

Square Roots

Square roots are mathematical expressions that represent a number which, when multiplied by itself, gives the original number. In the equation, the square root functions indicate that we are dealing with non-negative values, as square roots of real numbers are defined only for non-negative inputs. Understanding how to manipulate square roots is essential for solving equations involving them.
Video consigliato:
02:20
Imaginary Roots with the Square Root Property

Isolating Variables

Isolating variables is a fundamental algebraic technique used to solve equations. This involves rearranging the equation to get the variable of interest on one side, allowing for easier manipulation and solution. In the given problem, isolating the square root terms will help simplify the equation and make it solvable.
Video consigliato:
05:28
Equations with Two Variables

Squaring Both Sides

Squaring both sides of an equation is a common method used to eliminate square roots. When both sides of an equation are squared, it can simplify the equation, but it is crucial to check for extraneous solutions afterward, as squaring can introduce solutions that do not satisfy the original equation. This step is particularly relevant in the context of the given problem.
Video consigliato:
03:42
Linear Inequalities with Fractions & Variables on Both Sides
Pratica correlata
Domanda del libro di testo

Solve for x: xx3=9\(\sqrt\)[3]{x \(\sqrt{x}\)} = 9

662
views
Domanda del libro di testo

In Exercises 137–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation |x| = - 6 is equivalent to x = 6 or x = - 6.

627
views
Domanda del libro di testo

Find b such that (7x + 4)/b + 13 = x has a solution set given by {- 6}.

1248
views
Domanda del libro di testo

Exercises 141–143 will help you prepare for the material covered in the next section. If the width of a rectangle is represented by x and the length is represented by x + 200, write a simplified algebraic expression that models the rectangle's perimeter.

712
views
Domanda del libro di testo

Find b such that (4x - b)/(x - 5) = 3 has a solution set given by {Ø}.

803
views
Domanda del libro di testo

Solve without squaring both sides: 5 - (2/x) = √(5 - 2/x).

508
views