/*! 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 102 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 102

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \(3(x+4)=3(4+x)\) has precisely one solution.

Short Answer

Expert verified
The statement 'The equation \(3(x+4)=3(4+x)\) has precisely one solution' is false. The corrected statement is 'The equation \(3(x+4)=3(4+x)\) has infinite solutions.'

Step by step solution

01

- Analyze the equation

The equation given is \(3(x+4)=3(4+x)\) . The first step is to expand both sides of the equation by distributing 3 to \(x+4\) and \(4+x\).
02

- Simplify and compare

After distributing, the left side will be \(3x+12\) and the right side will be \(12+3x\) . If we rearrange the terms on the right hand side, we get \(3x+12\) which is same as left hand side. So, the equation \(3x+12 = 3x+12\) is always true for all values of \(x\). Hence, not only one solution exists.
03

- Correction of the statement

The original statement is false because it states there is precisely one solution. To correct the statement, it should state 'The equation \(3(x+4)=3(4+x)\) has infinite solutions.'

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!

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

Will help you prepare for the material covered in the next section. Is 6 a solution of \(4 y-7 \geq 5 ?\)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I prefer interval notation over set-builder notation because it takes less space to write solution sets.

Will help you prepare for the material covered in the next section. Solve: \(\quad x=4(90-x)-40\)

An HMO pamphlet contains the following recommended weight for women: "Give yourself 100 pounds for the first 5 feet plus 5 pounds for every inch over 5 feet tall." Using this description, which height corresponds to an ideal weight of 135 pounds?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I find that my answers involving \(\pi\) can vary slightly depending on whether I round \(\pi\) mid-calculation or use the \(\pi\) key on my calculator and then round at the very end.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.