Answer:
k = -240 or k = -1/240 depending on what the problem means.
Explanation:
This is what the equation you posted means:
1/3 k + 80 = 1/2 k + 120
1/3 k - 1/2 k = 40
2/6 k - 3/6 k = 40
-1/6 k = 40
k = -240
This may be what you meant:
1/(3k) + 80 = 1/(2k) + 120
1/(3k) - 1/(2k) = 40
2/(6k) - 3/(6k) = 40
-1/(6k) = 40
-1/6 = 40k
k = -1/240
Either way, there is a solution.