Question

see attachment :)

Answer 1

the triangles AEB and CEB are congruent by Side Angle Side Postulate

so side AB = side BD corresponding sides in congruent triangles are equal.

so

3x + 4 = 2x + 7

all you need to do is solve for x.

Answer 2

A perpendicular bisector divides the triangle into 2 smaller triangles of equal measures.
This means that AB = BD
So, all we need to do is equate their values and solve for x.
3x + 4 = 2x + 7
3x - 2x = 7 - 4
x = 3

So x = 3 which is the third option.