H is between G and I. GH = 7y + 3, HI = 3y - 5, and GI = 9y +7. What is the value of y?

Question

I need to know the value of Y but I just dont understand...

Answer 1

GH + HI = GI

7y + 3 + 3y - 5 = 9y + 7

10 y - 2 = 9y + 7

y - 2 = 7

y = 9

Check : GH = 7y + 3 = 7x9 + 3 = 66

HI = 3y-5 = 3x9 - 5 = 22

GH + HI = 66 + 22 = 88

GI = 9y + 7 = 9x9 + 7 = 88.

Mike

Answer 2

GH=HI

7y+3 = 3y-5

4y=-8

y=-2

GH=7y+3 = --14 + 3 = -11

HI = 3y-5 = --6-5=-11

But GH+HI=GI

-11 -11 does not equal 9(-2)+7 = -11

-22 does not equal -11

The lengths are negative, which is strange

and you can't set GH=HI and get GH+HI=GI

There's an inconsistency or contradiction in the problem if you copied it correctly.

Unless when it says H is half way between G and I, it means GHI is an equilateral triangle. H is equidistant from G and I, and then GH=HI=GI

But still you're in some strange space where distances are negative. GH can't equal HI, if the distances are positive 7y+3 = 3y-5 only if y = -2 which makes the distances negative