Sure! Let's solve the given equation step-by-step:
1. Understand the equation: The given equation is:
[tex]\[
\frac{x-7}{3} = \frac{x-1}{3}
\][/tex]
2. Eliminate the denominators: Since the denominators on both sides are equal, we can eliminate the fractions by multiplying both sides of the equation by 3:
[tex]\[
3 \cdot \frac{x-7}{3} = 3 \cdot \frac{x-1}{3}
\][/tex]
This simplifies to:
[tex]\[
x-7 = x-1
\][/tex]
3. Isolate the variable: To isolate \(x\), first, we subtract \(x\) from both sides of the equation:
[tex]\[
(x - 7) - x = (x - 1) - x
\][/tex]
Simplifying this yields:
[tex]\[
-7 = -1
\][/tex]
4. Analyze the result: The equation \(-7 = -1\) is a false statement. This implies that no value of \(x\) can satisfy the original equation.
Therefore, the equation [tex]\(\frac{x-7}{3} = \frac{x-1}{3}\)[/tex] has no solution.
