Question

Solve the following equations and check your results: $3m=5m-\dfrac{8}{5}$.

Answer 1

Hint: Multiply both the L.H.S and R.H.S by 5 to make the expression free from fraction. Now, take the terms containing ‘m’ to the left hand side and the constant terms to the right hand side. Find the value of m to get the answer.

Complete step-by-step solution -
We have been provided with the equation: $3m=5m-\dfrac{8}{5}$. We have to solve this equation, that means, we have to find the value of m.
As we can see that, this is a linear equation in one variable, which is m. Therefore,
Multiplying both sides by 5, we get,
$15m=25m-8$
Taking the terms containing ‘m’ to the L.H.S and the constant terms to the R.H.S, we get,
$\begin{align}
  & 15m-25m=-8 \\
 & \Rightarrow -10m=-8 \\
\end{align}$
Now, multiplying both sides by -1, we get,
$\begin{align}
  & 10m=8 \\
 & \Rightarrow m=\dfrac{8}{10} \\
\end{align}$
Cancelling the common terms in the fraction, we get,
$m=\dfrac{4}{5}$
Hence, the value of ‘m’ is $\dfrac{4}{5}$.
Now, it is said that we have to check the answer. That means we have to substitute the value of ‘m’ obtained in the equation and see whether it satisfies the equation or not. So, let us check.
Substituting, $m=\dfrac{4}{5}$ in the given equation, we get,
$L.H.S=3\times \dfrac{4}{5}=\dfrac{12}{5}$
And, $R.H.S=5\times \dfrac{4}{5}-\dfrac{8}{5}=\dfrac{20}{5}-\dfrac{8}{5}=\dfrac{12}{5}$
Clearly, L.H.S = R.H.S, therefore our answer is correct.

Note: One may note that we have been provided with a single equation only. The reason is that, we have to find the value of only one variable, that is ‘m’. So, if we have to solve an equation having ‘n’ number of variables then we should be provided with ‘n’ equations. Now, one can apply other methods also to solve this question. You can take the R.H.S term to the left hand side and take the L.C.M. Now, to remove the fraction, multiply both sides with ‘5’. The final answer will be the same.