Question

How do you solve for x in $\dfrac{1}{2}x=20$?

Answer 1

Hint: To solve the given equation in x which is given as: $\dfrac{1}{2}x=20$. We are going to rearrange the given equation in such a manner so that on the one side of the equation, only x terms are there and on the other side of the equation only constant terms are there. Then we will solve the equation in such a way so that on one side of the equation only x should be there and on the other side constant terms.

Complete step-by-step solution:
The equation given in the above problem is as follows:
$\dfrac{1}{2}x=20$
Now, we are going to rearrange the above equation in such a way so that on one side of the equation, only x terms are there and on the other side, only constant terms.
As you can see in the above equation that already on one side of the equation, only x term is there and on the other side constant term so now, we are going to make the coefficient of x in the above equation as 1 by multiplying 2 on both the sides and we get,
$\begin{align}
  & \Rightarrow \dfrac{1}{2}x=20 \\
 & \Rightarrow \dfrac{1}{2}\times 2x=20\times 2 \\
\end{align}$
In the L.H.S of the above equation, 2 will be cancelled out from the numerator and the denominator and we are left with:
$x=40$
Hence, we have solved the given equation and the value of x is 40.

Note: We can check the solution of the equation which we are getting is correct or not by substituting the value of x which we are getting above in the original equation and then see whether those values of y are satisfying the given equation or not.
The value of x which we have solved above is 40 so substituting this value of x in the above equation we get,
$\begin{align}
  & \Rightarrow \dfrac{1}{2}x=20 \\
 & \Rightarrow \dfrac{1}{2}\left( 40 \right)=20 \\
\end{align}$
Dividing 40 by 2 in the L.H.S of the above equation we get,
$\Rightarrow 20=20$
From the above, we can say that the value of x which we have solved is correct.