Answer:For the expression [tex]\frac{1}{4} k = 3 (-\frac{1}{4}k +3)[/tex] k = 9 is the required solution.Step-by-step explanation:Here, the given expression is [tex]\frac{1}{4} k = 3 (-\frac{1}{4}k +3)[/tex]Solving the above expression for k, we get:[tex]\frac{1}{4} k = 3 (-\frac{1}{4}k +3) \implies \frac{k}{4} = (\frac{-3}{4}k) + 9[/tex]or, [tex]\frac{k}{4} + (\frac{3}{4}k) = 9 \implies \frac{k + 3k}{4} = 9[/tex]or, [tex]\frac{4k}{4} = 9 \implies k =9[/tex]or, k = 9Hence for the expression [tex]\frac{1}{4} k = 3 (-\frac{1}{4}k +3)[/tex] k = 9 is the required solution.