let start by multiplying both sides by the LCD of all denominators, in this case that'd be 5, to do away with the denominators.
[tex]\bf \cfrac{1}{5}k-9=\cfrac{3}{5}k-7\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{5}}{5\left( \cfrac{1}{5}k-9 \right)=5\left( \cfrac{3}{5}k-7 \right)}\implies k-45=3k-35 \\\\\\ -45=2k-35\implies -10=2k\implies \cfrac{-10}{2}=k\implies -5=k[/tex]
