Question

Find x such that: - $\dfrac{-27}{x}=9$.

Answer 1

Hint: First of all cross multiply the terms by considering 1 as the denominator in the R.H.S. Take the terms containing the variable x to the L.H.S and all the constant terms to the R.H.S. Now, simplify both the sides with the help of simple arithmetic operations like addition and subtraction. Finally, divide both the sides with the coefficient of x and simplify the R.H.S to get the answer.

Complete step-by-step solution:
Here we have been provided with the equation $\dfrac{-27}{x}=9$ and we are asked to find the value of x. First let us simplify the expression.
$\because \dfrac{-27}{x}=9$
Cross multiplying the terms on both the sides by considering 1 in the denominator of the R.H.S we get,
$\begin{align}
  & \Rightarrow \dfrac{-27}{x}=\dfrac{9}{1} \\
 & \Rightarrow -27=9x \\
\end{align}$
Clearly we can see that the above expression is a linear equation in x, so let us find the value of x. Now, taking the term containing the variable x to the L.H.S. and taking the constant term to the R.H.S we get,
\[\Rightarrow -9x=27\]
Dividing both the sides with the coefficient of x, i.e. (-9), to make the coefficient of the variable equal to x we get,
\[\begin{align}
  & \Rightarrow x=\dfrac{27}{-9} \\
 & \therefore x=-3 \\
\end{align}\]
Hence, the value of x is -3.

Note: If you want to check the answer then just substitute the obtained value of x in the equation provided in the question. Solve for the L.H.S and R.H.S expression separately and if they are equal then our answer is correct otherwise there may be some calculation mistake which must be corrected. Note that the given expression is invalid for the value x = 0 because in the original equation we have x in the denominator.