Question

How do you solve $\dfrac{1}{2}x + 3 = 9$ ?

Answer 1

Hint: As per the question, we need to find the number which is represented by $x$. Equations like the question above $\dfrac{1}{2}x + 3 = 9$ are first degree equations, as the variable in the question has an exponent 1. What is the equation? – The answer to this is that the equals sign separates the equation into two parts and hence the left part is called as L.H.S ( Left Hand Side ) and the right part is called as R.H.S. ( Right Hand Side ), and as there is equal sign in between the L.H.S and R.H.S so they both need to be equal. Hence, in this question we need to find the number which the L.H.S equal to R.H.S.

Complete step by step answer:
 First we are going to rewrite the equation,
$\dfrac{1}{2}x + 3 = 9$
We know that any number multiplied with ‘1’ gets the answer as the number itself.
Again, by rewriting the equation we get,
$\dfrac{x}{2} + 3 = 9$
Now, here we are going to apply the property we can call it as addition-subtraction property. So that we generate an equivalent equation that has identical solutions. The addition- subtraction property states that if the same quantity is added to or subtracted from
the both sides of the equation, then the resulting equation is equivalent to the original equation.
Here, we are adding -3 to both the sides, we get
  $
\Rightarrow \dfrac{x}{2} + 3 - 3 = 9 - 3 \\
\Rightarrow \dfrac{x}{2} + {3} - {3} = 9 - 3 \\
 $
 Simplifying the above and by rewriting we get,
$ \Rightarrow \dfrac{x}{2} = 6$
Multiplying both sides by 2, so that we can get the value of ‘ x ’.
$ \Rightarrow 2 \times \dfrac{x}{2} = 6 \times 2$
$ \Rightarrow {2} \times \dfrac{x}{{{2}}} = 6 \times 2$
$ \Rightarrow x = 12$
So, the original equation solution is the number 12 that the number which was represented by x is 12 but to answer mathematically in the form of equation $x = 12$.

Note: For verifying you can substitute the solution in the original equation, if the Left Hand side comes out to be equal to the Right Hand side, then the answer is correct.
The symmetric property of equality can make our solving method easier; it states that if $x = y$. Then $y = x$, we always try to avoid the negative coefficient in our equation to solve this we apply division property with ‘-1 ’.