Question 259842
5/9x+6=-4/9x-2
assuming that you mean
5x/9+6=-4x/9-2
let's consolidate
add -6 to both sides
5x/9=-4x/9+4
multiply both sides by 9
5x=-4x+36
add 4x tbs
9x=36
x=4

if the 9x is the denominator then:

5/9x+6=-4/9x-2
multiply 6 and -2 by 9x/9x
5/9x+54x/9x=-4/9x-18x/9x
(5+54x)/9x=(-4-18x)/9x
multiply by 9x
5+54x=-4-18x
add 4
9+54x=-18x
divide by 9
1+6x=-2x
1=-8x
-1/8=x