Given houses of a row are numbered consecutively from 1 to 49.

i.e.  1,2,3,4,................,49

It forms an AP

where first term a = 1

common difference = d = 2-1 = 1

Number of terms n =49

Now according to question

                     S_x-1 = S₄₉ - S_x

            => (x-1)/2* {2*1 + (x-1-1)*1} = (49/2)*{2*1 + (49-1)1} -  (x/2)*{2*1 + (x-1)1} 

            => (x-1)/2* {2 + x - 2} = (49/2)*{2 + 48} -  (x/2)*{2 + x - 1}

            => x*(x-1)/2 = (49*50)/2 -  (x/2)*{x + 1} 

            => x*(x-1) = (49*50) -  x*{x + 1}

            => x² - x = 2450 - x² - x

           => 2x² = 2450

           => x² = 2450/2

           => x² = 1225  

           => x = √1225

           => x = 35

So the value of x is 35.