Pregunta
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

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

\( r = 2t \)

Solución

1. Start with the equation: \[ 3(r+t)=5r-t \] 2. Distribute \(3\) to both \(r\) and \(t\) on the left-hand side: \[ 3r + 3t = 5r - t \] 3. To collect like terms, subtract \(3r\) from both sides: \[ 3t = 2r - t \] 4. Add \(t\) to both sides to isolate the term with \(r\): \[ 3t + t = 2r \] 5. Simplify the left-hand side: \[ 4t = 2r \] 6. Divide both sides by \(2\) to solve for \(r\): \[ r = 2t \]

Respondido por UpStudy AI y revisado por un tutor profesional

error msg
Explicar
Simplifique esta solución

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!

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad