Question

Solve the linear equation $\dfrac{1}{9}\left( 2m-16 \right)=\dfrac{1}{3}\left( 2m+4 \right)$?

Answer 1

Hint: To solve the given equation we have to simplify the given equation furthermore. Certain transformations and substitutions should be made to get the equation simplified and to get the value of $m$. And finally verification should be done to check whether the value of $m$ we get is correct or not.

Complete step-by-step solution:
From the question it had been given that,
$\dfrac{1}{9}\left( 2m-16 \right)=\dfrac{1}{3}\left( 2m+4 \right)$
Now, to simplify further, multiply both sides of the equation by $9$.
By multiplying the equation both sides with $9$ we get,
$\dfrac{9}{9}\left( 2m-16 \right)=\dfrac{9}{3}\left( 2m+4 \right)$
$\Rightarrow 2m-16=3\left( 2m+4 \right)$
This will be more simplified into,
$\Rightarrow 2m-16=6m+12$
$\Rightarrow -4m=28$
$\Rightarrow m=-7$
Therefore the value of $m=-7$
Now, as we have already discussed above, we have to verify both the left hand side and right hand side of the equation to know whether we got the exact value or not.
Verification:
Left hand side: $\dfrac{1}{9}\left( 2m-16 \right)$
As we got the value of $m=-7$, substitute the value of $m=-7$ in the left hand side of the equation.
By substituting we get,
$\Rightarrow \dfrac{1}{9}\left( 2\left( -7 \right)-16 \right)$
$\Rightarrow \dfrac{1}{9}\left( -14-16 \right)$
$\Rightarrow \dfrac{-30}{9}$
$\Rightarrow \dfrac{-10}{3}$
Now, we have to verify the right hand side of the equation, right hand side of the equation is $\dfrac{1}{3}\left( 2m+4 \right)$
Now, substitute the value of $m=-7$ in the right hand side of the equation, by substituting the value of $m=-7$ we get,
$\Rightarrow \dfrac{1}{3}\left( 2\left( -7 \right)+4 \right)$
$\Rightarrow \dfrac{1}{3}\left( -14+4 \right)$
$\Rightarrow \dfrac{-10}{3}$
We can clearly observe that the left hand side and right hand side of the equation are equal.
Hence, verified.

Note: While answering questions of this type we should perform our calculations carefully and we should verify the answer is correct or not otherwise we may encounter a wrong answer due to wrong calculation and mark it. For answering questions of this type we should perform transformations and substitutions.