To solve the equation [tex]\(\frac{x}{5} = 25\)[/tex], follow these steps:
1. Identify the equation: [tex]\(\frac{x}{5} = 25\)[/tex].
2. Isolate the variable [tex]\(x\)[/tex]: We need to get [tex]\(x\)[/tex] by itself on one side of the equation. To do this, we can multiply both sides of the equation by 5, which is the denominator in the fractional expression [tex]\(\frac{x}{5}\)[/tex].
3. Multiply both sides by 5:
[tex]\[
\frac{x}{5} \times 5 = 25 \times 5
\][/tex]
4. Simplify both sides:
- On the left side, [tex]\(\frac{x}{5} \times 5\)[/tex] simplifies to [tex]\(x\)[/tex].
- On the right side, [tex]\(25 \times 5\)[/tex] simplifies to [tex]\(125\)[/tex].
Therefore, we have:
[tex]\[
x = 125
\][/tex]
5. Verify the solution: Substitute [tex]\(x = 125\)[/tex] back into the original equation to ensure it satisfies the equation.
[tex]\[
\frac{125}{5} = 25
\][/tex]
This is true since [tex]\(125 \div 5 = 25\)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{125}
\][/tex]
Therefore, the solution to the equation [tex]\(\frac{x}{5} = 25\)[/tex] is [tex]\(x = 125\)[/tex], which corresponds to option C.
