Solve the following equations and check your answer: x+9=13

Hint: In this question, we have been given an equation, which we can solve by adding -9 to both sides to find the value of x. Thereafter, we can put the obtained value of x in the LHS and then verify that the value in LHS equals that in RHS.

Complete step-by-step answer:
The given equation is
 \[x+9=13\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .\left( 1.1 \right)\]
We know that an equation remains valid if we add or subtract the same number both in the Left Hand Side (LHS) and Right Hand Side (RHS). Therefore, we should subtract a number on both sides such that only x remains on the LHS. As 9 is present as a separate term in LHS, we can subtract 9 from both sides in equation (1.1) to obtain
$\begin{align}
  & \left( x+9 \right)-9=13-9 \\
 & \Rightarrow x+9-9=4 \\
 & \Rightarrow x=4..................(1.2) \\
\end{align}$
Therefore, we obtain the value of x to be 4. Now, to verify that our answer is correct, we must put the value of x in the given equation and check that LHS=RHS.
Putting x=4 in the LHS of the given equation, we obtain
$LHS=x+9=4+9=13...................(1.3)$
However, as there is no term involving x in the Right Hand Side(RHS), the value of RHS remains unchanged at 13. Thus, we obtain
$RHS=13...................(1.4)$
Thus, from equation (1.3) and (1.4), as both RHS and LHS are equal to 13, we get $LHS=RHS$. Thus, the value of x=4 is verified to be correct.

Note: We should note that in equation (1.2), as 9 was present as a separate term, we could subtract 9 from both sides. However, if some non-zero number is multiplied to x, we can divide both sides by that number to make the LHS equal to x and equate it to RHS to find the value. However, we cannot divide both sides by zero as division by zero is undefined.