Question
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
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution is all real numbers.
Solution
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.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain
Simplify this solution
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.