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2kx-3k<2x+3kx

First goal is to have all the k's on the left hand side. So, let's subtract 3kx from both sides

2kx-3kx-3x<2x

Simplify

-kx-3k<2x *Factor out a k*

k(-x-3)<2x *Divide by (5x-3)*

k<2x/(-x-3)

The value is 1, because no matter what value you put in for x, the right hand side will be negative.

Therefore if k is 1, 1 is not less than a negative number. It is greater than a negative number. Therefore, k=1 is not a solution.

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