Solve for x:
-5/(2 x) = -5/6-7/(4 x)
-5/(2 x) = -5/(2 x) and -5/6-7/(4 x) = -5/6-7/(4 x):
-5/(2 x) = -5/6-7/(4 x)
Bring -5/6-7/(4 x) together using the common denominator 12 x:
-5/(2 x) = (-21-10 x)/(12 x)
Cross multiply:
-60 x = 2 x (-21-10 x)
Expand out terms of the right hand side:
-60 x = -42 x-20 x^2
Add 20 x^2+42 x to both sides:
20 x^2-18 x = 0
Factor x and constant terms from the left hand side:
2 x (10 x-9) = 0
Divide both sides by 2:
x (10 x-9) = 0
Split into two equations:
x = 0 or 10 x-9 = 0
Add 9 to both sides:
x = 0 or 10 x = 9
Divide both sides by 10:
x = 0 or x = 9/10
-5/(2 x) => -5/(2 0) = infinity^~
-5/6-7/(4 x) => -7/(4 0)-5/6 = infinity^~:
So this solution is incorrect
-5/(2 x) => -5/((2 9)/10) = -25/9
-5/6-7/(4 x) => -5/6-7/((4 9)/10) = -25/9:
So this solution is correct
The solution is:
Answer: | x = 9/10