Answer: The required solution for k in terms of h is [tex]k=\dfrac{6k-2h}{3}.[/tex]
Step-by-step explanation: We are given to solve the following equation for k in terms of h :
[tex]\dfrac{h-3k}{2k}=-\dfrac{3}{4}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given equation for k, we need to take all the other terms on the right-hand side and k on the left hand side of the equation.
From equation (i), we have
[tex]\dfrac{h-3k}{2k}=-\dfrac{3}{4}\\\\\\\Rightarrow 4(h-3k)=-3\times2k\\\\\Rightarrow -6k=4h-12k\\\\\Rightarrow k=\dfrac{4h-12k}{-6}\\\\\\\Rightarrow k=\dfrac{6k-2h}{3}.[/tex]
Thus, the required solution for k in terms of h is [tex]k=\dfrac{6k-2h}{3}.[/tex]
