/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 7 If \(x+y=2 x+2 y\), then \(4 x+4... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 7

If \(x+y=2 x+2 y\), then \(4 x+4 y\) is: (A) 1 (B) 0 (C) 2 (D) 4 (E) Cannot be determined

Short Answer

Expert verified
The value of \( 4x + 4y \) is 0, which corresponds to option (B).

Step by step solution

01

Identify and simplify the given equation

We have the equation: \[ x + y = 2x + 2y \] First, simplify by moving all terms to one side of the equation. Subtract \( x + y \) from both sides to get: \[ x + y - x - y = 2x + 2y - x - y \]}
02

Combine like terms

On combining like terms on both sides, we get:\[ 0 = x + y \] This implies that:\[ x + y = 0 \]
03

Find the value of the expression

We need to determine the value of \( 4x + 4y \). Using the equation \( x + y = 0 \), multiply both sides by 4 to get:\[ 4(x + y) = 4 \times 0 \]This simplifies to:\[ 4x + 4y = 0 \]
04

Determine the correct option

From the simplified form, \( 4x + 4y = 0 \). Therefore, the correct answer is (B) 0.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Algebra
Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. These symbols often represent numbers and are used to describe relationships and solve equations. In this problem, we use algebraic expressions and equations to find the desired value. Understanding how to manipulate these symbols is crucial for simplifying and solving algebraic problems efficiently.
Equation Simplification Made Easy
Equation simplification is about making an equation easier to solve. It involves combining like terms, removing unnecessary parts, and using basic arithmetic operations. Here, we start with the given equation:
\[ x + y = 2x + 2y \] We can move all terms to one side to get
\[ x + y - x - y = 2x + 2y - x - y \] This leads to a simplified form where we combine like terms, resulting in
\[ 0 = x + y \] Simplifying equations is a step-by-step process that makes it easier to solve and understand the problem.
Problem-Solving Steps
Effective problem-solving in math requires following a logical sequence of steps. Let's review the steps taken:
  • Identify and simplify the given equation.

  • Combine like terms on both sides of the equation.

  • Use the simplified equation to find the required expression value.

  • Determine the correct option based on your calculations.
Using these steps keeps you organized and ensures you don't miss any important details. It also helps you systematically break down complex problems into manageable parts.
Expression Evaluation
Evaluating expressions involves substituting known values into an expression and performing the operations to find the result. In this problem, after simplifying the equation to \[ x + y = 0 \] we need to find the value of \[ 4x + 4y \] We know that \[ x + y = 0 \] so we multiply both sides by 4:
\[ 4(x + y) = 4 \times 0 \] This simplifies to:
\[ 4x + 4y = 0 \] This step involves straightforward arithmetic, but it's crucial to understand the principles of substitution and operations when evaluating algebraic expressions.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In those days you had no real alternative but too enter the same trade or profession as your father. A. too enter the same trade or profession as your father. B. to enter the same trade or profession as your father. C. to enter the trade or profession like your father. D. enter the trade or profession same as your father. E. take up the trade or profession equal to your fathers

. The book is about Sardinia, and the author has been all about that beautiful island. A. about Sardinia, and the author has been all about B. around Sardinia, and the author has been all around C. about Sardinia, and the author has been all around D. around Sardinia, and the author has been all about E. round Sardinia, and the author has been all round

He was totally engrossed in his work when the telephone started to ring. A. when B. while C. hardly Answer D. because E. as

Is \(\mathrm{n}\) divisible by 3 with no remainder? (1) \(\mathrm{n}-3\) is divisible by 3 with integer result (2) \(\mathrm{n}-21\) is divisible by 3 with integer result A. 1 alone, not 2 alone B. 2 alone, not 1 alone C. 1 and 2 together (need both) D. 1 alone or 2 alone E. 1 and 2 together are not sufficient

Is \(y>3 x+2 ?\) (1) \(y>4 x\) (2) \(x>2\) A. 1 alone, not 2 alone B. 2 alone, not 1 alone C. 1 and 2 together (need both) D. 1 alone or 2 alone E. 1 and 2 together are not sufficient
See all solutions

Recommended explanations on English Textbooks

Essay Writing Skills

Read Explanation

English Grammar Summary

Read Explanation

Single Paragraph Essay

Read Explanation

Rhetorical Analysis Essay

Read Explanation

Synthesis Essay

Read Explanation

Lexis and Semantics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.