Question

Can you help me find the step by step answer to the problem that is circled?

Answer 1

Given

$3x+2k=\frac{15y}{9w-18v}$

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:

$\begin{gathered} (3x+2k)^{-1}=(\frac{15y}{9w-18v})^{-1} \\ \frac{1}{3x+2k}=\frac{9w-18v}{15y} \end{gathered}$

Second, multiply both sides by 15y

$\begin{gathered} 15y\cdot\frac{1}{3x+2k}=15y\cdot\frac{9w-18v}{15y} \\ \frac{15y}{3x+2k}=9w-18v \end{gathered}$

Third, add 18v to both sides of the equal sign

$\begin{gathered} \frac{15y}{3x+2k}+18v=9w-18v+18v \\ \frac{15y}{3x+2k}+18v=9w \end{gathered}$

Finally, divide both sides by 9 and simplify

$\begin{gathered} \frac{\frac{15y}{3x+2k}}{9}+\frac{18v}{9}=\frac{9w}{9} \\ (\frac{15y}{3x+2k}\cdot\frac{1}{9})+2v=w \\ \frac{1\cdot15y}{9(3x+2k)}+2v=w \\ \frac{15y}{27x+18k}+2v=w \\ \frac{5y}{9x+6k}+2v=w \end{gathered}$

The expression written for w is

$w=\frac{5y}{9x+6k}+2v$