if you notice the rhombus, the tickmarks on CE and EA means they're both equal.
the ∡DEA is a right angle, if that angle is a right angle made by those segments, that means angles ∡BEA and ∡BEC are also right angles.
the segment of BE is shared by the the triangle BEC and the triangle BEA, and therefore is equal for both.
what the dickens does all that mean?
well, those two triangles have a SIDE, then an ANGLE, and then another SIDE which are congruent to each other, meaning the triangles are congruent by Side Angle Side, namely SAS.
if the triangles are congruent, all their sides are congruents as well, thus BC = BA and therefore,
[tex]\bf 6x + 11 = 11x - 9\implies 20=5x\implies \cfrac{20}{5}=x\implies 4=x[/tex]
