Given
[tex]3x+2k=\frac{15y}{9w-18v}[/tex]
To solve for w, the objective is to leave the w-term on one side of the equal sign and all other terms on the other side.
First, apply the exponent -1 to both sides of the expression to invert both terms:
[tex]\begin{gathered} (3x+2k)^{-1}=(\frac{15y}{9w-18v})^{-1} \\ \frac{1}{3x+2k}=\frac{9w-18v}{15y} \end{gathered}[/tex]
Second, multiply both sides by 15y
[tex]\begin{gathered} 15y\cdot\frac{1}{3x+2k}=15y\cdot\frac{9w-18v}{15y} \\ \frac{15y}{3x+2k}=9w-18v \end{gathered}[/tex]
Third, add 18v to both sides of the equal sign
[tex]\begin{gathered} \frac{15y}{3x+2k}+18v=9w-18v+18v \\ \frac{15y}{3x+2k}+18v=9w \end{gathered}[/tex]
Finally, divide both sides by 9 and simplify
[tex]\begin{gathered} \frac{\frac{15y}{3x+2k}}{9}+\frac{18v}{9}=\frac{9w}{9} \\ (\frac{15y}{3x+2k}\cdot\frac{1}{9})+2v=w \\ \frac{1\cdot15y}{9(3x+2k)}+2v=w \\ \frac{15y}{27x+18k}+2v=w \\ \frac{5y}{9x+6k}+2v=w \end{gathered}[/tex]
The expression written for w is
[tex]w=\frac{5y}{9x+6k}+2v[/tex]
