Isosceles trapezoid geometry question

sides DE are parallel to GF.
DE=4x-2
EF=3X+2
FG=5X-3
GD=2X+5.
what is the value of x?
how do you solve this?

an isosceles trapezoid has two parallel sides: the base and the top
since it is isosceles two of the sides will equal, if it was the base and top it would not be a trapezoid, so that means the sides that are not parallel to each other must equal each other

since DE is parallel to GF and it is a isosceles trapezoid, sides EF and GD are equal to each other
(EF) 3x + 2 = (GD) 2x + 5
then you solve for x
x=3

check
(3)(3) + 2 = 2(3) + 5
11=11

then you check to make sure the other values make sense
EF=11 , GD=11
DE=4(3) - 2
DE=10
GF=5(3)-3
GF=12
the top is DE, the base is GF, and the sides are EF and GD

IDK XD!