Question

How do you solve the relational equation $\dfrac{5}{-x-6}=\dfrac{2}{x}$ ?

Answer 1

Hint: First do the cross multiplication. Then try to separate the variables and constants. Keep all the terms containing the variable ‘x’ on the left side of the equation and all the constant terms on the right side of the equation. Do the necessary calculation to get the value of ‘x’.

Complete step-by-step solution:
Solving the relational equation means, we have to find the value of ‘x’, for which the equation gets satisfied.
The relational equation we have $\dfrac{5}{-x-6}=\dfrac{2}{x}$
Cross multiplying, we get
$\begin{align}
  & \Rightarrow 5\times x=2\times \left( -x-6 \right) \\
 & \Rightarrow 5x=-2x-12 \\
\end{align}$
We have to keep all the terms containing ‘x’ on the left side of the equation and all constant terms on the right side.
As the constant term is already on the right side, so bringing $-2x$ to the left side of the equation, we get
$\begin{align}
  & \Rightarrow 5x+2x=-12 \\
 & \Rightarrow 7x=-12 \\
 & \Rightarrow x=\dfrac{-12}{7} \\
\end{align}$
This is the required solution of the given question.

Note: Cross multiplication should be the first approach for solving such questions. The constant terms and the terms containing ‘x’ should be separated as constants on the right side of the equation and the terms containing ‘x’ on the right side of the equation. Necessary calculation and simplification should be done to get the value of ‘x’.