Question

How do you solve for $a$: in $p = a + b + 3c$?

Answer 1

Hint: In this question, we are asked to find the solution in terms of the variable $a$. Firstly, we will simplify the given equation with the help of algebraic operations in such a way that the terms which does not contain `$a$’ in it should be at the right hand side of the equation and only the term with the variable ‘$a$’ in it should be on the left hand side. So we subtract the terms which do not contain the term ‘$a$’ on both sides of the equation and obtain the required result.

Complete step-by-step answer:
Given an expression of the form $p = a + b + 3c$
We are asked to solve for the variable ‘$a$’ in the above expression.
We simplify the given expression with the help of algebraic operations, so that the terms containing the variable ‘$a$’ will be on the left hand side and rest other terms on the right hand side of the equation.
Now we solve for the variable ‘$a$’.
Let us consider the given equation $p = a + b + 3c$ …… (1)
By subtraction property of equality, subtract $b$ from both sides of the equation (1), we get,
$ \Rightarrow p - b = a + b + 3c - b$
Rearranging this we get,
$ \Rightarrow p - b = a + 3c + b - b$
Combining the like terms $b - b = 0$
Hence we have,
$ \Rightarrow p - b = a + 3c + 0$
$ \Rightarrow p - b = a + 3c$
Now again by subtraction property of equality, subtract $3c$ from both sides we get,
$ \Rightarrow p - b - 3c = a + 3c - 3c$
Combining the like terms $3c - 3c = 0$.
Hence we have,
$ \Rightarrow p - b - 3c = a + 0$
$ \Rightarrow p - b - 3c = a$
This can also be written as,
$ \Rightarrow a = p - b - 3c$
Hence the required solution for the equation $p = a + b + 3c$ in terms of the variable ‘$a$’ is given by $a = p - b - 3c$.

Note:
If the equation satisfies the expression of ‘$a$’, then it is the required solution for the given problem. We need to be careful while taking the terms to the other side. When transferring any variable or number to the other side, the sign of the same will be changed to its opposite sign.
It is important to know the following basic facts.
An equation remains unchanged or undisturbed if it satisfies the following conditions.
(1) If L.H.S. and R.H.S. are interchanged.
(2) If the same number is added on both sides of the equation.
(3) If the same number is subtracted on both sides of the equation.
(4) When both L.H.S. and R.H.S. are multiplied by the same number.
(5) When both L.H.S. and R.H.S. are divided by the same number.