Line bc has an equation of a line y = 2x + 3, and line ef has an equation of a line y = negative one over 2x + 4. these two equations represent

a. parallel lines because the slopes of the lines are equal
b. perpendicular lines because the slopes are opposite reciprocals
c. the same line when graphed
d. lines that intersect, but not at a right angle

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4