Question

Given $ak=v+w,$ how do you solve for a?
(a) Dividing each side by a
(b) By simplifying
(c) Dividing each side by k
(d) All of the above

Answer 1

Hint: We are given the equation $ak=v+w,$from which we have to find the value of a. So, to get the solution, we will start with dividing the both sides of the equation by k. From which we can get the left side of the equation left only with a. We will try to simplify the right side to get our needed solution.

Complete step by step solution:
According to the question, we are given, $ak=v+w,$
So, we will start with, dividing each side of the equation by k to solve for a while keeping the equation balanced.
$\dfrac{ak}{k}=\dfrac{v+w}{k}$
Now, cancelling k in the left hand side,
\[a=\dfrac{v+w}{k}\]
Now, we can also separate the right hand side of the equation into two parts with $\dfrac{v}{k}$and $\dfrac{w}{k}$ . So, we can write that,
\[a=\dfrac{v}{k}+\dfrac{w}{k}\]

So, the correct answer is “Option c”.

Note: Here in this problem, we are trying to find the solution of the equation which is a monomial. A monomial is an expression in algebra that contains one term, like 3xy. Monomials include: numbers, whole numbers and variables that are multiplied together, and variables that are multiplied together. Any number, all by itself, is a monomial, like 5 or 2,700. A monomial can also be a variable, like m or b.