To solve the equation \( 25(x + 15) = 26 \), we will follow these steps:
Step 1: Distribute the 25
First, we will distribute the 25 on the left side of the equation:
\[ 25 \cdot x + 25 \cdot 15 = 26 \]
This simplifies to:
\[ 25x + 375 = 26 \]
Step 2: Isolate the term with x
Next, we want to isolate the term containing \( x \). To do this, we subtract 375 from both sides of the equation:
\[ 25x + 375 - 375 = 26 - 375 \]
This results in:
\[ 25x = 26 - 375 \]
Calculating the right side:
\[ 26 - 375 = -349 \]
So we have:
\[ 25x = -349 \]
Step 3: Solve for x
Now, we divide both sides by 25 to solve for \( x \):
\[ x = \frac{-349}{25} \]
Step 4: Simplify the fraction (if necessary)
Since \( -349 \) and \( 25 \) have no common factors besides 1, we can leave the fraction as it is. For better understanding, we can convert it into a decimal, if necessary:
\[ x \approx -13.96 \]
Step 5: Conclusion
Thus, the final solution for \( x \) is:
\[ \boxed{\frac{-349}{25}} \quad \text{or} \quad \boxed{-13.96} \]
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