Question

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

Answer 1

Given

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

Second, multiply both sides by 15y

`\begin{gathered} 15y\cdot(1)/(3x+2k)=15y\cdot(9w-18v)/(15y) \\ (15y)/(3x+2k)=9w-18v \end{gathered}`

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

`\begin{gathered} (15y)/(3x+2k)+18v=9w-18v+18v \\ (15y)/(3x+2k)+18v=9w \end{gathered}`

Finally, divide both sides by 9 and simplify

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

The expression written for w is

`w=(5y)/(9x+6k)+2v`