Question

Solve the following linear equation:
$\dfrac{12}{7}\left( x-7 \right)=24+8x$

Answer 1

Hint: The equation given in the question is a linear equation in one variable. For solving the problem, first of all, open the bracket on the left-hand side of the equation then write the terms containing x on the one side and the terms which are not containing x on the other side of the equation and then simplify it.

Complete step-by-step solution -
The equation given in the question that we have to solve is:
$\dfrac{12}{7}\left( x-7 \right)=24+8x$
Now, we are going to open the bracket on the left hand side of the equation.
$\dfrac{12}{7}x-12=24+8x$
Rearranging the above equation in such a way that the terms containing x on the left hand side of the equation and the other constant terms on the right hand side of the equation we get,
$\dfrac{12}{7}x-8x=24+12$
On taking L.C.M of 7 on the left hand side of the equation we get,
$\dfrac{12x-56x}{7}=36$
Multiplying 7 on both the sides we get,
$\begin{align}
  & -44x=36\left( 7 \right) \\
 & -44x=252 \\
\end{align}$
Dividing -44 on both the sides we get,
$x=-\dfrac{252}{44}=-\dfrac{63}{11}$
From the above, we have solved the value of x as $-\dfrac{63}{11}$.
Hence, the solution of the given equation gives the value of $x=-\dfrac{63}{11}$.

Note: You can verify the value of x that we have got above substituting the value of x in the given equation:
$\dfrac{12}{7}\left( x-7 \right)=24+8x$
The value of x that we have got above is equal to $-\dfrac{63}{11}$ so plugging this value of x in the above equation will give:
$\dfrac{12}{7}\left( \left( -\dfrac{63}{11} \right)-7 \right)=24+8\left( -\dfrac{63}{11} \right)$
Taking L.C.M of 11 on both the sides we get,
$\begin{align}
  & \dfrac{12}{7}\left( \dfrac{-63-77}{11} \right)=\dfrac{264-504}{11} \\
 & \Rightarrow -\dfrac{1}{7}\left( \dfrac{140\times 12}{11} \right)=\dfrac{-240}{11} \\
\end{align}$
In the above equation, 11 will be cancelled out on both the sides.
$-\dfrac{1}{7}\left( 140\times 12 \right)=-240$
Minus signs will be cancelled out on both the sides and solving individually the left hand and right hand side of the equation.
$\dfrac{1}{7}\left( 140\times 12 \right)=240$
  Solving L.H.S of the above equation we get,
$\begin{align}
  & \dfrac{1}{7}\left( 140\times 12 \right) \\
 & =20\times 12 \\
 & =240 \\
\end{align}$
R.H.S is equal to 240.
Hence, L.H.S is equal to R.H.S.
So, the value of x that we have got is verified.