The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x (Hint: `S_[x-1]=S_[49]-S_x`)

Explanation

To solve the problem, we need to find a value of \( x \) such that the sum of the house numbers before house \( x \) is equal to the sum of the house numbers after house \( x \).

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have houses numbered from 1 to 49. We need to find \( x \) such that:
\[
S_{x-1} = S_{49} - S_x
...