Acceso
Prima
Hogar Banco de preguntas Matemáticas Álgebra
Pregunta
upstudy study bank question image url

Solve the equation. Then determine whether the equation is ar equation. \( 4 x+27=9(x+3)-5 x \) What is the solution? Select the correct choice below and, if ne

Ask by Hardy Ross. in the United States
Jan 26,2025

Solución de tutoría real

Respuesta verificada por el tutor

Responder

The equation is true for all real numbers \( x \), meaning there are infinitely many solutions.

Solución

Let's solve the equation step by step and determine its nature. **Given Equation:** \[ 4x + 27 = 9(x + 3) - 5x \] **Step 1: Expand and Simplify Both Sides** 1. Expand the right-hand side (RHS): \[ 9(x + 3) = 9x + 27 \] 2. Substitute back into the equation: \[ 4x + 27 = 9x + 27 - 5x \] 3. Combine like terms on the RHS: \[ 9x - 5x = 4x \] 4. Now, the equation is: \[ 4x + 27 = 4x + 27 \] **Step 2: Solve for \( x \)** Subtract \( 4x \) from both sides: \[ 4x + 27 - 4x = 4x + 27 - 4x \] \[ 27 = 27 \] **Analysis:** The equation simplifies to a true statement \( 27 = 27 \), which means that the original equation holds true for **all real numbers** \( x \). There is no unique solution; instead, there are **infinitely many solutions**. **Conclusion:** - **Solution:** The equation is true for all real numbers \( x \) (infinitely many solutions). - **Type of Equation:** It is an **identity** (a statement that is always true). **Answer Summary:** All real numbers satisfy the equation. Since it is always true, the equation has infinitely many solutions.

Revisado y aprobado por el equipo de tutoría de UpStudy

error msg
Explicar
Simplifique esta solución

Extra Insights

First, let's simplify and solve the equation step-by-step. Start with \( 4x + 27 = 9(x + 3) - 5x \). Distributing the \( 9 \) gives us \( 4x + 27 = 9x + 27 - 5x \). This simplifies to \( 4x + 27 = 4x + 27 \). Since both sides of the equation are equal, this means any value for \( x \) will satisfy the equation, making it an identity. Therefore, the solution is that there are infinitely many solutions, as the equation holds for all values of \( x \). Now, keep in mind that this type of equation is a special case called an identity, which occurs when the equation simplifies to a true statement regardless of the variable's value! This kind of equation is super interesting because it reflects a balance that exists in many algebraic contexts. If you're ever in doubt while solving equations, remember to double-check each step! Many common mistakes come from mishandling negative signs or distributing incorrectly. Always simplify both sides to ensure you're comparing the same expressions—this can save you from the headaches of getting stuck in the calculations!

preguntas relacionadas

Solve the following equation. \[ 6 x+6=30 \] Select the correct choice below and, if necessary, fill in the answer box. A. The solution is \( \square \) . (Type an integer or a simplified fraction.) B. The solution set is \( (-\infty, \infty) \). C. There is no solution.
Álgebra United States Jan 27, 2025
1.4 Hoeveel terme is daar in die ry? Beantwoord die vae hieronder vir ry A, B, C en D. A. \( 9 x+8 ; 2 x-6 ; x-8 \) B: \( 4 x-3 ; x ; 2 x-5 \) \( 7 x+1 ; x+3 ; x-5 \) 21 Bepaal die waardes van \( x \) waarvoor hierdie terme meetkundige rye vort 22 Bepaal 'n formule vir die \( n \) de term van elke ry. 23 Bepaal die waarde van die tiende term van elke ry.
Álgebra South Africa Jan 27, 2025
Solve. \( 21-\frac{2}{3} x=-\frac{2}{3} x+21 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( x=\square \) (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. There is no solution.
Álgebra United States Jan 27, 2025
S. \( \frac{1}{4} a^{3} b^{12} \times \frac{16}{5} a^{3} b^{2} \) 2. \( \frac{2\left(2 a^{4}\right)^{3}}{16 a^{12}} \) 3. \( \frac{6 a^{4}+9 a^{4}}{5 a^{2}} \) 4. \( \frac{3 a^{3} \times 5 a^{5}}{\left(5 a^{3}\right)^{2}} \) 5. \( P^{x-1} \cdot P^{x+1} \)
Álgebra South Africa Jan 27, 2025
1. ¿Cuál es la ecuación que representa el enunciado "El cuadrado de un número más dos veces el mismo número es igual a cuatro veces dicho número? 2. Anota una ecuación de la forma \( a x^{2}+b x=0 \) 3. Anota una ecuación de la forma \( a x^{2}+c=0 \) 4. Anota una ecuación de la forma \( a x^{2}+b x+c=0 \) 5. En las sigulentes ecuaciones identifica los valores de los coeficientes \( a, b, c \) a. \( x^{2}+3 x=-25 \) b. \( 2 x=-35+x^{2} \) c. \( 3 x^{2}+5 x-3=x^{2}-30 \) d. \( x^{2}+x=2 x^{2}+10 \) 6. Menciona en que consiste el discriminante, para que sirve y los posibles valores que puede tener. 7. En las siguientes ecuaciones, encuentra el discriminante e indica cuantas soluciones hay. a) \( x^{2}-2 x+2=0 \) b) \( x^{2}-6 x+9=0 \) c) \( x^{2}+x=6 \) d) \( x^{2}+4 x+4=0 \) 8. Resuelve las siguientes ecuaciones incompletas por despeje a) \( x^{2}-81=0 \) b) \( 3 x^{2}=75 \) c) \( x^{2}-\frac{1}{4}=0 \) d) \( 6 x^{2}-150=0 \) 9. Resuelve las siguientes ecuaciones aplicando el factor común. a) \( 2 x^{2}=12 x \) b) \( 4 x^{2}+12 x=0 \) c) \( 2 x^{2}=x \) d) \( x^{2}+5 x=0 \) 10. Resuelve las siguientes ecuaciones cuadráticas completas por factorización a) \( x^{2}-4 x-45=0 \) b) \( x^{2}=4 x-3 \) c) \( x^{2}-3 x-18=0 \) d) \( x^{2}-10 x=24 \)
Álgebra Mexico Jan 27, 2025

Latest Algebra Questions

Solve the following equation. \( \begin{array}{l}3-\mathrm{x}=7\end{array} \) \[ \begin{array}{l}\text { Select the correct choice below and, if necessary, fill in the answer box. } \\ \text { (Type an integer or a simplified fraction.) } \\ \text { B. The solution set is }(-\infty, \infty) \text {. There is no solution. } \\ \text { C. The }\end{array} \]
Álgebra United States Jan 27, 2025
Solve the following equation. \[ 2 x-7=0 \] Select the correct choice below and, if necessary, fill in the answer box. A. The solution is (Type an integer or a simplified fraction.) B. The solution set is \( (-\infty, \infty) \). C. There is no solution.
Álgebra United States Jan 27, 2025
Faclorise fully \( 125 \mathrm{~m}^{3}+15 \mathrm{~m} \)
Álgebra South Africa Jan 27, 2025
Solve. \( 21-\frac{2}{3} x=-\frac{2}{3} x+21 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( x=\square \) (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. There is no solution.
Álgebra United States Jan 27, 2025
S. \( \frac{1}{4} a^{3} b^{12} \times \frac{16}{5} a^{3} b^{2} \) 2. \( \frac{2\left(2 a^{4}\right)^{3}}{16 a^{12}} \) 3. \( \frac{6 a^{4}+9 a^{4}}{5 a^{2}} \) 4. \( \frac{3 a^{3} \times 5 a^{5}}{\left(5 a^{3}\right)^{2}} \) 5. \( P^{x-1} \cdot P^{x+1} \)
Álgebra South Africa Jan 27, 2025
Anterior Próximo
¡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