Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 7

Which of the following inequalities is the solution to the inequality \(3 x+32\) C. \(x<-2\) D. \(x<-1\) E. No solution exists

Short Answer

Expert verified
D. \(x < -1\)

Step by step solution

01

- Subtract x from both sides

Start by isolating the variable on one side. Subtract x from both sides of the inequality: \[ 3x + 3 - x < x + 1 - x \] This simplifies to: \[ 2x + 3 < 1 \]
02

- Subtract 3 from both sides

Subtract 3 from both sides of the inequality to further isolate the term with the variable: \[ 2x + 3 - 3 < 1 - 3 \] This simplifies to: \[ 2x < -2 \]
03

- Divide both sides by 2

Divide both sides of the inequality by 2 to solve for x: \[ \frac{2x}{2} < \frac{-2}{2} \] This simplifies to: \[ x < -1 \]

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

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

solving inequalities
Inequalities are similar to equations but instead of an equals sign, they use inequality signs like <, >, ≤, and ≥. To solve inequalities, we often use algebraic manipulation to isolate the variable.
For example, in the exercise given, we start with the inequality: \(3x+3We follow specific steps to isolate the variable:
  • Subtract x from both sides: \(3x+3-x
  • Subtract 3 from both sides: \(2x+3-3<1-3\), which simplifies to: \(2x<-2\).
  • Divide both sides by 2: \(\frac{2x}{2}< \frac{-2}{2}\), which simplifies to: \(x<-1 \).
Each step involves an arithmetic operation that helps to isolate x and find the solution to the inequality.
GMAT preparation
Preparing for the GMAT involves honing your skills in various areas, including the ability to solve inequalities. This concept is essential because GMAT questions often test your understanding of algebra and your ability to perform algebraic manipulations efficiently.
Here are some tips for preparing for the GMAT:
  • Practice regularly: The more you practice solving inequalities, the more comfortable you will become.
  • Understand each step: Make sure you grasp why each algebraic manipulation is performed.
  • Time management: Ensure you can solve these problems quickly and accurately, as time management is crucial in the GMAT.
By following these tips, you will improve your ability to solve inequalities and your overall GMAT performance.
algebraic manipulation
Algebraic manipulation refers to the process of rearranging and simplifying algebraic expressions to solve equations and inequalities.
In the exercise, the following algebraic manipulations were applied:
  • Subtracting a term from both sides: This is done to simplify the inequality and isolate the variable. For example, subtracting x from both sides in the original equation.
  • Subtracting a constant: This helps in further isolating the variable term. In the exercise, we subtracted 3 from both sides to simplify the inequality.
  • Dividing by a coefficient: This is the final step to isolate x. For instance, dividing both sides by 2.
These manipulations ensure that we can solve for the variable step by step and arrive at the correct solution: \(x<-1\). Understanding these operations is key to mastering algebra and solving GMAT questions effectively.

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

The advertised position received 1,200 applicants but none of the applying candidates were suitable. A. none of the applying candidates B. none of the affected candidates C. none of the candidates affected D. none of the candidates applying E. none of these

If \(5 x+4 y=22\) and \(3 x+5 y=21\), then \(x\) is: A. 2.1 B. 2.2 C. 2.5 D. 2.0 E. 2.8

Which of the following statements, if true, would prove the case that the vast majority of collectors find their collections worth less than they originally paid for them? A. The world’s most expensive stamps have doubled in value in the last 12 years. B. Over the years, high-quality stamps have risen in value at a rate equal to the growth rate of the rest of the economy. C. The collecting price for a stamp is determined more by rarity than original posting value. D. Commemorative stamps from the 1940s command the best prices. E. After decades, some new issues command higher prices for collecting than their original posting.

They in September consulted on the issue extensively and began immediately implementing the new strategy. A. They in September consulted on the issue extensively and began immediately implementing the new strategy. B. They consulted in September on the issue extensively and immediately began implementing the new strategy. C. In September they consulted extensively on the issue and immediately began implementing the new strategy. D. They consulted on the issue extensively in September and immediately began implementing the new strategy. E. They consulted on the issue extensively in September and began immediately implementing the new strategy.

For which values of \(x\) is \(2 x^2-3 x\) greater than \(x\) ? A. \(1>x>3\) B. \(0>x>2\) C. \(-4
See all solutions

Recommended explanations on English Textbooks

Key Concepts in Language and Linguistics

Read Explanation

Email

Read Explanation

5 Paragraph Essay

Read Explanation

Cues and Conventions

Read Explanation

Morphology

Read Explanation

History of English Language

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.

Sign-up for free