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The given equation is:

\[
\frac{53x - 4}{25} = 625
\]

### Steps to solve for \( x \):

1. **Multiply both sides by 25** to eliminate the denominator:
   \[
   53x - 4 = 625 \times 25
   \]
   \[
   53x - 4 = 15625
   \]

2. **Add 4** to both sides to isolate the term with \( x \):
   \[
   53x = 15625 + 4
   \]
   \[
   53x = 15629
   \]

3. **Divide by 53** to solve for \( x \):
   \[
   x = \frac{15629}{53}
   \]
   \[
   x = 295
   \]

Thus, the solution is \( x = 295 \).

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Would you like more details or have any questions?

Here are some related questions you might find useful:
1. How do you simplify equations with fractions?
2. What are the properties of equalities used in this solution?
3. Can you explain how to deal with equations involving negative exponents?
4. What happens if we have an unknown in both the numerator and denominator?
5. What are other methods to solve equations like this?

**Tip**: Always check your solution by substituting the value of \( x \) back into the original equation to ensure it holds true.

Learn how to solve the equation (53x - 4) / 25 = 625 with a detailed step-by-step solution. This problem focuses on key algebraic concepts such as linear equations and equality properties. Suitable for students in Grades 8-10.

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