Pregunta
Solve. \[ \begin{array}{l}29-\frac{6}{7} x=-\frac{6}{7} x+29 \\ \text { Select the correct choice below and, if necessary, fill in the answer box to complete your choice. } \\ \text { A. } x=\square \text { (Type an integer or a simplified fraction.) } \\ \text { B. The solution is all real numbers. } \\ \text { C. There is no solution. }\end{array} \text {. } \]
Ask by May Hardy. in the United States
Jan 27,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The solution is all real numbers.
Solución
To solve the equation:
\[
29 - \frac{6}{7}x = -\frac{6}{7}x + 29
\]
Let's simplify both sides:
1. **Left Side:**
\[
29 - \frac{6}{7}x
\]
2. **Right Side:**
\[
-\frac{6}{7}x + 29
\]
Notice that both sides of the equation are identical:
\[
29 - \frac{6}{7}x = -\frac{6}{7}x + 29
\]
This means that for any real number \( x \), the equation holds true. There is no restriction on \( x \) because both sides are exactly the same, making the equation an identity.
**Conclusion:** The solution is all real numbers.
**Answer:**
B. The solution is all real numbers.
Revisado y aprobado por el equipo de tutoría de UpStudy
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The Deep Dive
To solve the equation \( 29 - \frac{6}{7} x = -\frac{6}{7} x + 29 \), we first notice that both sides of the equation are equal to each other because they are identical. This means that any value of \( x \) will satisfy the equation. Therefore, the solution to the equation is all real numbers. So, the correct choice is: B. The solution is all real numbers.
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