Solve and check your answer: $\dfrac{2}{3}x + 3 = 11$

Hint: Here, an equation is given, and we are asked to solve it. To solve an equation means to find the value of the unknown variable in that equation. In our given equation, there is one unknown variable $x$ and we need to find the value of it.To find it, we just need to keep the variable in one side and constants in the other side by the use of simple mathematical calculation. To verify the obtained solution, we need to substitute it in the place of the variable and check whether it satisfies the equation.

Complete step-by-step answer:
We are given an equation and we need to solve the equation.
The word solve means to find the value of the variable $x$ in the given equation.
Here the given equation is $\dfrac{2}{3}x + 3 = 11$
So, from this, we need to find the value of $x$
To find the value of $x$ here, we need to subtract both sides of the equation by $3$
$
  \dfrac{2}{3}x + 3 - 3 = 11 - 3 \\
  \dfrac{2}{3}x = 8 \\
 $
Now, let us multiply both sides of the equation by $3$
$
  \dfrac{2}{3}x \times 3 = 8 \times 3 \\
  2x = 24 \\
 $
Now we need to divide both the sides by $2$
$
  \dfrac{{2x}}{2} = \dfrac{{24}}{2} \\
  x = 12 \\
 $
Now we get the value of $x$ to be $12$
We are also asked to verify the obtained solution.
To verify a solution for a particular equation, we need to substitute the respective solution in the given equation and need to verify whether the left-hand side is equal to the right-hand side of the equation.
Here the equation is $\dfrac{2}{3}x + 3 = 11$ and the obtained solution is $12$.
So, let’s substitute $12$ in the place of $x$ in the equation $\dfrac{2}{3}x + 3 = 11$.
Substituting, we get
$
  \dfrac{2}{3} \times 12 + 3 = 11 \\
  \dfrac{{24}}{3} + 3 = 11 \\
  8 + 3 = 11 \\
  11 = 11 \\
 $
We can see that the left-hand side is equal to the right-hand side of the equation.
This proves that $12$ is the solution of the equation $\dfrac{2}{3}x + 3 = 11$.

Note: We need to analyze the equation and decide the appropriate arithmetic operation to be used to find the solution. Here we use subtraction, multiplication, and division to find our solution.
The usage of the arithmetic operation may change according to the given equation.
The second and third steps of solving the equation can also be combined
That is, instead of doing multiplication and division separately it can be clubbed by multiplying $\dfrac{3}{2}$ on both sides
$
  \dfrac{2}{3}x \times \dfrac{3}{2} = 8 \times \dfrac{3}{2} \\
  x = \dfrac{{24}}{2} \\
  x = 12 \\
 $