Question
upstudy study bank question image url

c. \( 3(r+t)=5 r-t \quad \) for \( r \)

Ask by Cummings Bartlett. in the United States
Mar 16,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

\( r = 2t \)

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

To solve for \( r \), let's start by distributing the 3 on the left side: \[ 3r + 3t = 5r - t. \] Now, we want to get all terms involving \( r \) on one side and constant terms on the other. Rearranging gives us: \[ 3t + t = 5r - 3r \] \[ 4t = 2r. \] Dividing both sides by 2, we find: \[ r = 2t. \] So, the solution for \( r \) in terms of \( t \) is \( r = 2t \). But hey! Did you know that algebra has roots in ancient civilizations? The Babylonians and Egyptians were some of the first to use early forms of algebraic concepts more than 4,000 years ago. They employed geometric methods for problem-solving and laid the groundwork for the algebra we utilize today! In the realm of problem-solving, it's essential to keep track of your variable terms and constants when rearranging equations. A common mistake is to lose track of negative signs or to improperly distribute terms. Always double-check your arithmetic—those small slips can lead you down the wrong path in solving equations!

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