Question

How do you solve for $b$ in $a = 2b$?

Answer 1

To solve this question, we need to use the concept of multiplication or division in simple equations. This is typically when the variable is already on one side of the equation, but there is either more than one of the variables. For instance, we have two variables here $a$and $b$and the digit 2 is multiplied with variable $b$on the right hand side of the equation.

Complete step by step answer:
We are given $a = 2b$.
Now, to find the variable $b$, we need to remove the digit 2 which is multiplied with it. This can be done by dividing the right hand side by 2. However, it is important to know that we need to perform any arithmetic operation on both the sides of the equation.
Therefore, we will divide both the sides of the equation by 2.
$\Rightarrow \dfrac{a}{2} = \dfrac{{2b}}{2}$
Now, we know that when there is the same number in the numerator and the denominator, it gets cancelled out. Therefore, here, we can cancel out the digit 2 on the right hand side of the equation.
Which will give us the equation:
$\Rightarrow \dfrac{a}{2} = b$
We also know that equality is reflexive which means we can alternate the places of right hand side and left hand side.
Therefore, we can rewrite our equation as:
$\Rightarrow b = \dfrac{a}{2}$
Thus, by this method, we can obtain the value of $b$as $\dfrac{a}{2}$.

Note:
It is important to keep in mind that while solving a simple equation, we need to think of the equation as a balance. Thus, if we do something to one side of the equation, we must do the same thing to the other side.
Doing the same thing to both sides of the equation keeps the equation balanced. For example, we have divided both the sides by 2 in this problem.