Determine the value of x in this equation. You can choose the method you use to solve, but you must list ALL steps and the solution.

25(x+15)=26

1 answer

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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