Question

How do you solve for \[B\] in \[S = 2B + Ph?\]

Answer 1

Hint: This question involves the arithmetic operations like addition/ subtraction/ multiplication/ division. We need to find the value \[B\] from the given equation. We need to know the basic algebraic formulae to solve this problem. We need to know how to separate \[B\] from the given equation.

Complete step-by-step answer:
The given equation is shown below,
 \[S = 2B + Ph \to \left( 1 \right)\]
We would find the value \[B\] from the above equation. For that, we move the term \[Ph\] from RHS to LHS of the equation
 \[\left( 1 \right) \to S = 2B + Ph\]
 \[S - Ph = 2B\]
(When we move \[ + Ph\] from RHS to LHS it converts into \[ - Ph\] .)
The above equation can also be written as,
 \[2B = S - Ph \to \left( 2 \right)\]
To simplify the above equation move the term \[2\] from LHS to RHS of the equation. ( \[2\] Is involved in the multiplication process with \[B\] . When we move it to another side of the equation it will involve division operation.)So, we get
 \[\left( 2 \right) \to 2B = S - Ph\]
 \[B = \dfrac{{S - Ph}}{2} \to \left( 3 \right)\]
We know that,
 \[\dfrac{{a - b}}{n} = \dfrac{a}{n} - \dfrac{b}{n}\]
So, the equation \[\left( 3 \right)\] becomes,
 \[\left( 3 \right) \to B = \dfrac{{S - Ph}}{2}\]
 \[B = \dfrac{S}{2} - \dfrac{{Ph}}{2}\]
So, the final answer is,
 \[B = \dfrac{S}{2} - \dfrac{{Ph}}{2}\]
So, the correct answer is “ \[B = \dfrac{S}{2} - \dfrac{{Ph}}{2}\] ”.

Note: This type of questions involve the arithmetic operations like addition/ subtraction/ multiplication/ division. Also, remember the basic algebraic formulae to solve this type of question. When one term moves from left-hand side to right-hand side(or) right-hand side to left-hand side of the equation the following changes will occur according to the arithmetic operations which is involved by the mentioned term,
The operation of addition will be converted into the operation of subtraction.
The operation of subtraction will be converted into the operation of addition.
The operation of multiplication can be converted into the operation of division.
The operation of division can be converted into the operation of multiplication.