Let's solve the equation \( 5(5t + 1) = 25t - 7 \).

### Step 1: Expand the left side
Distribute the 5 on the left-hand side:
\[
5 \times 5t + 5 \times 1 = 25t + 5
\]
So the equation becomes:
\[
25t + 5 = 25t - 7
\]

### Step 2: Simplify the equation
Now, let's subtract \( 25t \) from both sides:
\[
25t + 5 - 25t = 25t - 7 - 25t
\]
This simplifies to:
\[
5 = -7
\]

### Conclusion:
The result \( 5 = -7 \) is a contradiction, which means the equation has **no solution**.

Would you like any details or have any questions about this solution?

Here are 5 related questions:
1. How do you solve linear equations with one variable?
2. What does it mean when an equation has no solution?
3. Can a linear equation have infinitely many solutions?
4. How do you solve equations that involve parentheses?
5. What are common errors to avoid when solving linear equations?

**Tip:** Always simplify and combine like terms on both sides of the equation before attempting to isolate the variable.

Discover how to solve the linear equation 5(5t + 1) = 25t - 7 with a detailed step-by-step solution. This problem highlights key algebraic concepts such as the distributive property and solving equations with no solution. Perfect for students in Grades 8-10.

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