Question
upstudy study bank question image url

Use indirect reasoning to show that there is no whole number, \( n \), which solves the equation \( 6 n+14=31 \). odd Is the number 6 n even or odd? odd is the sum \( 6 n+14 \) even or odd? even Based on the above answers, why is there no whole number, \( n \), that solves the equation \( 6 n+14=31 \) ? A. Both sides of the equation are always odd. B. Both sides of the equation are always even. C. The left side of the equation is always even and the right side is always odd. D. The right side of the equation is always even and the left side is always odd. Theretore, \( n \) cannot be a whole number. (

Ask by Daniels Campbell. in the United States
Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

There is no whole number \( n \) that solves the equation \( 6n + 14 = 31 \) because the left side is always even while the right side is always odd.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Beyond the Answer

The key to solving the equation \(6n + 14 = 31\) lies in the parity of both sides. We know that \(6n\) is even since any whole number multiplied by 6 is even. When we add 14 (which is also even), the entire left-hand side remains even. On the other side, 31 is an odd number. Since an even number can never equal an odd number, we conclude that there is no whole number \(n\) that satisfies the equation. Thus, the correct reasoning is that the left side \(6n + 14\) is always even, while the right side \(31\) is odd, confirming that we can't have a solution where both sides are equal. Hence, option C is correct: "The left side of the equation is always even and the right side is always odd."

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy