Let M be a middlepoint of HI and L be a middlepoint of HJ (because ML is a midsegment of HIJ). Since L is a middlepoint of HJ, you have that JL=HL.
If JL = 5x – 7 and LH = 2x + 5, then
5x-7=2x+5
5x-2x=5+7
3x=12
x=4.
When L is a middlepoint of another triangle side, you can say nothing about JL and LH.
