Domanda del libro di testo
Perform the indicated operations and write the result in standard form. (1 + i)/(1 + 2i) + (1 - i)/(1 - 2i)
899
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 95a
Evaluate x2 - x for the value of x satisfying 4(x - 2) + 2 = 4x - 2(2 - x).
Guida verificata passo dopo passo1
Step 1: Simplify both sides of the equation 4(x - 2) + 2 = 4x - 2(2 - x). Expand the terms using the distributive property: 4(x - 2) becomes 4x - 8, and -2(2 - x) becomes -4 + 2x. Rewrite the equation as 4x - 8 + 2 = 4x - 4 + 2x.
Step 2: Combine like terms on both sides of the equation. On the left-hand side, combine -8 and +2 to get -6, so the left-hand side becomes 4x - 6. On the right-hand side, combine -4 and 2x to get 4x + 2x - 4, which simplifies to 6x - 4. The equation now reads: 4x - 6 = 6x - 4.
Step 3: Isolate the variable x. Subtract 4x from both sides to eliminate the 4x term on the left-hand side: -6 = 2x - 4. Then, add 4 to both sides to isolate the term with x: -6 + 4 = 2x, which simplifies to -2 = 2x.
Step 4: Solve for x by dividing both sides of the equation by 2: x = -2 / 2, which simplifies to x = -1.
Step 5: Substitute x = -1 into the expression x^2 - x to evaluate it. Replace x with -1: (-1)^2 - (-1). Simplify the terms: (-1)^2 is 1, and -(-1) is +1. The expression becomes 1 + 1. Simplify further to find the result.
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:
3mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Solving Linear Equations
To find the value of x in the equation 4(x - 2) + 2 = 4x - 2(2 - x), one must isolate x by simplifying both sides. This involves distributing terms, combining like terms, and rearranging the equation to solve for x. Understanding how to manipulate linear equations is essential for determining the correct value of x.
Video consigliato:
04:02
Solving Linear Equations with Fractions
Substituting Values
Once the value of x is determined, it can be substituted back into the expression x^2 - x. Substitution is a fundamental algebraic technique that allows one to evaluate expressions based on known values. This step is crucial for finding the final result of the expression after solving the equation.
Video consigliato:
5:48Solving Systems of Equations - Substitution
Evaluating Quadratic Expressions
The expression x^2 - x is a quadratic expression, which can be evaluated by plugging in the value of x obtained from the previous steps. Understanding how to compute quadratic expressions involves recognizing the operations of squaring a number and performing basic arithmetic. This concept is vital for arriving at the final numerical answer.
Video consigliato:
03:11Evaluating Algebraic Expressions
Pratica correlata
Domanda del libro di testo
In Exercises 91–100, find all values of x satisfying the given conditions. and
656
views
Domanda del libro di testo
Solve each equation in Exercises 83–108 by the method of your choice.
904
views
Domanda del libro di testo
In Exercises 95–99, perform the indicated operations and write the result in standard form. 4/(2 + i)(3 - i)
1121
views
Domanda del libro di testo
Solve each equation in Exercises 83–108 by the method of your choice.
945
views
Domanda del libro di testo
In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions.
1515
views