Let's solve the equation \( 7 - (5t - 13) = -25 \).

### Step 1: Distribute the negative sign
First, distribute the negative sign across the terms inside the parentheses:

\[
7 - 5t + 13 = -25
\]

### Step 2: Combine like terms
Next, combine the constants on the left side of the equation:

\[
(7 + 13) - 5t = -25
\]
\[
20 - 5t = -25
\]

### Step 3: Isolate the term with \( t \)
Subtract 20 from both sides to move the constant term to the right side:

\[
-5t = -25 - 20
\]
\[
-5t = -45
\]

### Step 4: Solve for \( t \)
Finally, divide both sides by \(-5\):

\[
t = \frac{-45}{-5} = 9
\]

### Solution
The solution to the equation is \( t = 9 \).

Would you like more details or have any questions?

Here are some related questions:
1. What if the equation had been \( 7 + (5t - 13) = -25 \)?
2. How does distributing a negative sign affect an equation?
3. Can this technique be applied to systems of equations?
4. What happens if the equation includes fractions?
5. How can we check if our solution is correct?

**Tip:** Always simplify the equation as much as possible before solving for the variable.

Learn how to solve the equation 7 - (5t - 13) = -25 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations and the distributive property. Suitable for students in Grades 7-9.

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