Question

How do you solve: $\dfrac{1}{3}\left( 6+x \right)-5=12$?

Answer 1

Hint: Multiply both the sides of the given equation with 3 to remove the fractional term. Now, rearrange the terms of the given equation by leaving the terms containing the variable x to the L.H.S. and taking the constant terms to the R.H.S. Now, use simple addition, subtraction to simplify the R.H.S. Make the coefficient of x equal to 1 and accordingly change the R.H.S. to get the answer.

Complete step by step solution:
Here, we have been provided with the equation: $\dfrac{1}{3}\left( 6+x \right)-5=12$ and we are asked to solve this equation. That means we have to find the value of x.
$\because \dfrac{1}{3}\left( 6+x \right)-5=12$
Multiplying both the sides with 3 to remove the fraction in the L.H.S we get,
$\begin{align}
  & \Rightarrow \left( 6+x \right)-15=36 \\
 & \Rightarrow x+6-15=36 \\
\end{align}$
As we can see that the given equation is a linear equation in one variable which is x. So, leaving the terms containing the variable x to the L.H.S. and taking the constant terms to the R.H.S., we get,
\[\begin{align}
  & \Rightarrow x=15+36-6 \\
 & \Rightarrow x=45 \\
\end{align}\]

Hence, the value of x is 45.

Note: Here, it was not necessary to multiply both the sides with 3 at the initial step of the solution, you can also simplify the L.H.S by multiplying the constant with the terms inside the bracket. But you can notice that if we do so then the coefficient of x will become a fraction and to remove it we have to multiply both the sides with 3. So, either way you have to multiply both the sides with 3. You can check the answer by substituting the obtained value of x in the equation provided in the question. You have to simplify the L.H.S. by substituting x = 45 and if it equals 12 then our answer is correct.