Question

Solve the equation:
$\dfrac{2x}{3}=18$

Answer 1

Hint: Multiply both sides of the equation by 3. Then divide both sides of the equation by 2 and hence find the value of x. Verify your answer.

Complete step-by-step answer:
Before solving the question, we need to understand the process of solving an equation.
The solution of an equation remains unchanged if, on both sides, we add a certain quantity.
The solution of an equation remains unchanged if, on both sides, we subtract a certain quantity.
The solution of an equation remains unchanged if, on both sides, we multiply a certain non-zero quantity.
The solution of an equation remains unchanged if, on both sides, we divide a certain non-zero quantity.
We perform one or more of the above operations till LHS = x and RHS = some quantity.
Now, consider the equation
$\dfrac{2x}{3}=18$
The solution of the equation will remain unchanged if, on both sides, we multiply by 3.
Multiplying both sides of the equation by 3, we get
$\dfrac{2x}{3}\times 3=18\times 3\Rightarrow 2x=54$
The solution of the equation will remain unchanged if, on both sides, we divide by 2.
Dividing both sides of the equation by 2, we get
$\begin{align}
  & \dfrac{2x}{2}=\dfrac{54}{2} \\
 & \Rightarrow x=27 \\
\end{align}$
Hence the solution of the equation is x = 27

Note: Verification: If on substituting the value of x LHS = RHS, then that value of x is the solution of the equation.
We have LHS $=\dfrac{2}{3}\times 27=18$
RHS = 18
Hence, LHS = RHS
Hence our answer is verified to be correct.