I need help with the first question

Subtract 2k from both sides.

4k−3−2k=2k+5−2k

2k−3=5

Add 3 to both sides.

2k−3+3=5+3

2k=8

Divide both sides by 2.

2k /2 =8/2

k=4

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