The figure appears to be a parallelogram with diagonals AC and BD with E as the point of intersection of the two diagonals and also the midpoint.
Diagonal AC has segments AE measuring 3x + 1 and EC measuring x + 25. Since point E is the midpoint of the mentioned diagonal, therefore, we can say that the segments AE and EC should be congruent.
We get,
[tex]\text{ AE = EC}[/tex]Let's use this relationship to find x.
[tex]\text{ AE = EC}[/tex][tex]\text{ 3x + 1 = x + 25}[/tex][tex]\text{ 3x + 1 - x - 1 = x + 25 - x - 1}[/tex][tex]\text{ 2x = 24}[/tex][tex]\text{ }\frac{\text{2x}}{2}\text{ = }\frac{\text{24}}{2}[/tex][tex]\text{ x = 12}[/tex]Therefore, x = 12.