Question

Solve for w4/6 = w/9Simplify your answer as much as possible.

Answer 1

Solving an equation

We want to find the value of w, so the following equation is true:

`(4)/(6)=(w)/(9)`

Since both sides of the equation are equal, we must do the same on both sides, so they keep equal.

We want to leave w in only one side of the equation.

Then we want to bring 9 of the division to the left side so w can be alone in the right sides.

In order to do so we multiply both sides by 9:

`\begin{gathered} 9\cdot(4)/(6)=9\cdot(w)/(9) \\ \downarrow\text{right side} \\ 9\cdot(w)/(9)=(9w)/(9)=w \\ \downarrow left\text{ side} \\ 9\cdot(4)/(6)=(36)/(6)=6 \end{gathered}`

Then, we have that:

`\begin{gathered} 9\cdot(4)/(6)=9\cdot(w)/(9) \\ \downarrow \\ 9\cdot(4)/(6)=w \\ \downarrow \\ 6=w \end{gathered}`

Answer: w = 6