Question

How do you solve $\dfrac{2}{3w}=\dfrac{2}{15}+\dfrac{12}{5w}$?

Answer 1

Hint: In this problem we need to calculate the solution of the given equation i.e., the value of $w$ for which the given equation is satisfied. Firstly, we will rearrange the terms in the given equation so that all the terms having variable $w$ at one place and all the constant terms are at one place. Now we will consider the LCM and simplify the equation. After that we will use appropriate arithmetic operations to solve the given equation.

Complete step by step solution:
Given equation, $\dfrac{2}{3w}=\dfrac{2}{15}+\dfrac{12}{5w}$.
Shifting the term $\dfrac{12}{5w}$ which is right hand side to left hand side and changing the sign of the term, so that all the terms having variables are at one side, then we will get
$\Rightarrow \dfrac{2}{3w}-\dfrac{12}{5w}=\dfrac{2}{15}$
Considering the LCM of the terms $3w$, $5w$ and performing subtraction of fractions in the above equation, then we will get
$\begin{align}
  & \Rightarrow \dfrac{5\times 2-3\times 12}{15w}=\dfrac{2}{15} \\
 & \Rightarrow \dfrac{10-36}{15w}=\dfrac{2}{15} \\
 & \Rightarrow -\dfrac{12}{15w}=\dfrac{2}{15} \\
\end{align}$
In the above equation we can observe that $15$ is in denominator for the both the fraction on both sides of the equation. So, cancelling the denominator $15$ on both sides, then we will have
$\Rightarrow -\dfrac{12}{w}=2$
In the above equation we have $w$ in division, so multiplying $w$ on both sides of the above equation, then we will get
$\begin{align}
  & \Rightarrow -w\times \dfrac{12}{w}=2\times w \\
 & \Rightarrow -12=2w \\
\end{align}$
In the above equation we have $2$ in multiplication, so dividing the above equation with $2$ on both sides, then we will have
$\begin{align}
  & \Rightarrow -\dfrac{12}{2}=\dfrac{2w}{2} \\
 & \Rightarrow w=-6 \\
\end{align}$
Hence the solution for the given equation $\dfrac{2}{3w}=\dfrac{2}{15}+\dfrac{12}{5w}$ is $w=-6$.

Note:
We can also solve the above problem by following another method after getting $-\dfrac{12}{w}=2$. We can use cross multiplication and simplify the equation to get the result.
$\begin{align}
  & \Rightarrow \dfrac{-12}{2}=w \\
 & \Rightarrow w=-6 \\
\end{align}$
From both the methods we got the same result.