Question

How do you solve for variable w in the equation v = lwh?

Answer 1

Hint: Consider v, l, and h as constant terms. Now, divide both sides of the equation with the product of l and h to make the coefficient of w equal to 1. The expression thus obtained will be our answer.

Complete step by step answer:
Here, we have been provided with the equation v = lwh and we are asked to solve for the variable w.
Now, as we can see that there are four letters v, w, l, and h in which the only w is considered as the variable according to the question. So, we are going to consider l, v, and h as the constant terms. Now, to solve for the variable w means that we have to keep this variable w at one of the sides, i.e., L.H.S. or R.H.S., with its coefficient equal to 1. Let us keep w in the L.H.S, so we have,
\[\Rightarrow lwh=v\]
It can be written as: -
\[\Rightarrow \left( lh \right)w=v\]
Clearly, we see that the coefficient of w is \[\left( lh \right)\] and we need to make it equal to 1. So, dividing both the sides with \[\left( lh \right)\] we get,
\[\Rightarrow \dfrac{\left( lh \right)w}{\left( lh \right)}=\dfrac{v}{lh}\]
Canceling the common factors in the L.H.S. we get,
\[\Rightarrow w=\dfrac{v}{lh}\]
Hence, the value of w is \[\dfrac{v}{lh}\].

Note:
 One may note that there is no particular reason for assuming l, h, and v as constants. Even if we consider them as variables the method of solving the equation and the answer will not change. You must know the meaning of solving an equation and how to solve any linear equation.