-9/58=(2y-(3y+4))/(7y-(2-5y))

Solve for y:
-9/58 = (-4-y)/(12 y-2)

 

-9/58 = (-4-y)/(12 y-2) is equivalent to (-4-y)/(12 y-2) = -9/58:
(-4-y)/(12 y-2) = -9/58

 

Cross multiply:
58 (-4-y) = -9 (12 y-2)

 

Expand out terms of the left hand side:
-232-58 y = -9 (12 y-2)

 

Expand out terms of the right hand side:
-232-58 y = 18-108 y

 

Add 108 y+232 to both sides:
50 y = 250

 

Divide both sides by 50:
Answer: |  y = 5

-9/58=(2y-(3y+4))/(7y-(2-5y))

 

 

\(\frac{-9}{58}=\frac{2y\;\;-1(3y+4)}{7y\;\;-1(2-5y)}\\ \frac{-9}{58}=\frac{2y\;\;-3y-4}{7y\;\;-2+5y}\\ \frac{-9}{58}=\frac{-y\;\;-4}{12y\;\;-2}\\ \frac{-9}{58}=\frac{-(y\;\;+4)}{2(6y\;\;-1)}\qquad \mbox{note that }6y-1\ne0\quad so\;\;\;\;y\ne \frac{1}{6}\\ -9*2(6y-1)=58*-1*(y+4)\\ 9*2(6y-1)=58*(y+4)\\ 9(6y-1)=29(y+4)\\ 54y-9=29y+116\\ 25y=125\\ y=5\)

 

-9/58=(2y-(3y+4))/(7y-(2-5y))

check:

(2*5-(3*5+4))/(7*5-(2-5*5)) = -0.1551724137931034 = -9/58

 

 

RHS=(2*6-(3*6+4))/(7*6-(2-5*6) = -0.1428571428571429​

 

LHS=-9/58= -0.1551724137931034