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Chapter 5: Problem 29

If \(3 x+y=2 x-y\), then \(x+y\) is: A. \(-y\) B. \(-\mathrm{x}\) C. \((2 x-y) / 3\) D. \(x / 2-y / 3\) E. Cannot be determined

Short Answer

Expert verified
A. \(-y\)

Step by step solution

01

- Set Up the Equation

Start with the given equation: \[ 3x + y = 2x - y \]
02

- Isolate Terms Involving x and y

Move all terms involving x to one side and all terms involving y to the other side of the equation: \[ 3x - 2x = -y - y \]
03

- Simplify the Equation

Combine like terms: \[ x = -2y \]
04

- Express x in Terms of y

We found that: \[ x = -2y \]
05

- Calculate x + y

Substitute the expression for x back into the expression for x + y: \[ x + y = -2y + y \]
06

- Simplify the Expression

Combine the terms: \[ x + y = -y \]

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Key Concepts

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

Algebra Problem Solving
Algebra problem solving is a key skill for the GMAT. Understanding how to manipulate equations to find unknowns is essential. In the given problem, we start by setting up our equation based on the information provided: 3x + y = 2x - y. Next, rearrange the equation to isolate x and y on different sides. Subtracting 2x from both sides, we get: 3x - 2x + y = -y. Then, moving all y terms to one side, we simplify to: x = -2y. Finally, substituting x = -2y into the expression for x + y, we get -2y + y = -y. This demonstrates how each algebra step builds upon the previous to find the solution.
Graduate Management Admission Test
The GMAT tests your problem-solving abilities within a limited time. Algebra questions like the given exercise test your capacity to work with equations. Success requires familiarity with mathematical principles and speed. Being proficient in solving algebra problems allows you to score higher. The given sample problem illustrates a straightforward method to isolate and solve for variables, showcasing the typical algebraic manipulations expected on the test. Practice problems help reinforce these techniques, ensuring you can efficiently solve similar equations during the exam.
Equation Manipulation
Equation manipulation involves rearranging equations to isolate variables. By moving terms from one side to another, you keep the equation balanced. In the given exercise, starting with 3x + y = 2x - y: We needed to isolate x by subtracting 2x from both sides to yield x + y = -y. Simplifying further with the right steps lets us solve for x or y. Mastery of these skills allows one to untangle complex equations more easily. Always ensure each step logically follows from the previous. This technique is crucial on the GMAT to quickly and accurately solve problems.
Mathematical Reasoning
Mathematical reasoning is about understanding and applying logical steps to reach a solution. Starting from 3x + y = 2x - y, we reason that combining like terms helps isolate x and y. Moving terms yields x + y = -y, showing x = -2y. Therefore, in the context of x + y, substituting gives -2y + y = -y. This logical step-by-step reasoning is critical for problem-solving on the GMAT. Each step logically connects the problem statement to the solution, demonstrating clear and systematic mathematical thinking needed for test success.

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