Let's solve the given equation step-by-step:
Given equation:
[tex]\[
\frac{x}{5} - \frac{x}{5} = 4
\][/tex]
Step 1: Simplify the equation
Notice that [tex]\(\frac{x}{5}\)[/tex] and [tex]\(\frac{x}{5}\)[/tex] are the same terms. Therefore, when you subtract [tex]\(\frac{x}{5}\)[/tex] from [tex]\(\frac{x}{5}\)[/tex], it results in:
[tex]\[
\frac{x}{5} - \frac{x}{5} = 0
\][/tex]
So the equation simplifies to:
[tex]\[
0 = 4
\][/tex]
Step 2: Analyze the simplified equation
The equation [tex]\(0 = 4\)[/tex] is clearly a contradiction because zero does not equal four. This means that there is no value of [tex]\(x\)[/tex] that can satisfy this equation.
Conclusion:
Since [tex]\(0 = 4\)[/tex] is a contradiction, the original equation [tex]\(\frac{x}{5} - \frac{x}{5} = 4\)[/tex] has no solutions. Therefore, there is no value of [tex]\(x\)[/tex] that can make this equation true.
Thus:
[tex]\[
\boxed{\text{There is no solution to the equation} \frac{x}{5} - \frac{x}{5} = 4 \text{ as it simplifies to } 0 = 4, \text{ which is a contradiction.}}
\][/tex]
