Question

If \(3 y+x<0\) : A. \(y<-x / 3\) B. \(-y>x / 3\) C. \(y<-x / 3\) and \(-y>x / 3\) D. \(2 x>y / 6\) E. None of the above

Short answer

A. \( y < -\frac{x}{3} \)

Step-by-step solution

- Identify the Inequality

Start with the given inequality: \[3y + x < 0\]

- Isolate y

To isolate y, subtract x from both sides: \[3y < -x\]

- Solve for y

Divide both sides by 3 to solve for y: \[y < -\frac{x}{3}\]

- Review the Options

Compare the simplified inequality to the options provided. Option A, \( y < -\frac{x}{3} \), matches our result.

Key concepts

inequalities

Inequalities describe the relationship between two values when they are not equal but are instead greater than, less than, greater than or equal to, or less than or equal to each other. In the exercise, we started with the inequality \[3y + x < 0\]. This tells us that the sum of three times the value of y and the value of x must be less than zero. To manage these expressions, always consider the correct order of operations and ensure you isolate the variable correctly. Dealing with inequalities is much like solving equations, but with an important difference: if you multiply or divide by a negative number, the inequality sign reverses direction.

algebra

Algebra involves working with symbols, usually letters, to solve problems. The exercise provided is a classic example where we use algebraic techniques to isolate a variable and find its value. Let's break it down further:

• We started with the expression: \[3y + x < 0\].
• To isolate y, we needed to get rid of x on the left-hand side by performing the operation on both sides of the inequality: \[3y < -x\].
• Then, we divided both sides by 3 to isolate y: \[y < -\frac{x}{3}\].
Understanding these basic algebraic manipulations helps us work through more complex problems by breaking them down into simpler steps.

graduate management admission test

The GMAT, or Graduate Management Admission Test, is a standardized test used by many business schools to assess the qualifications of applicants for advanced study in business and management. It involves various sections, including quantitative, verbal, and analytical writing tasks. Problem-solving questions like the inequality problem we discussed are typical of the quantitative section.

• The quantitative section tests mathematical skills and understanding of fundamental concepts.
• It includes questions on arithmetic, algebra, geometry, and word problems.
• Understanding inequalities and being able to isolate variables and solve for them is crucial for doing well in this section.

test preparation

Preparing for the GMAT should involve a blend of strategy and practice. To advance, here are some key tips:

• Practice regularly: Frequently practicing GMAT problems helps you get accustomed to the question formats and time constraints.
• Understand the concepts: Don’t just memorize steps; focus on understanding the underlying mathematical principles.
• Time management: Work on managing your time efficiently during the test so you can adequately address each question.
• Review mistakes: Always review the solutions to problems you got wrong to understand your mistakes and avoid repeating them.
• Use quality materials: Ensure that you are using reputable and up-to-date preparation materials and resources.

Following these tips can help boost your confidence and improve your performance.