2k-3/-5>7 is treated slightly differently from an equality, for example -1<0, and adding 1 to each side preserves the inequality: 0<1. But if we multiply both sides by -1 we get 0<-1, which is false. 0>-1 is true. Therefore, we must reverse the inequality if we multiply the equation in the problem by -5: 2k-3<-35. So 2k<-32 (adding 3 to both sides). And the answer is k<-16. Put a value of k=-17 (this value is less than -16) in the original equation to check it out: -34-3/-5=-37/-5, which is the same as 37/5 which is greater than 7. So k<-16 fits the problem.