Question

Therefore, the equation 1/3k + 80 = 1/2k + 120 has no solution for k?

Answer 1

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.