Question

How do you solve for L in $32\text{LW = V}$?

Answer 1

Hint: In this question, we need to find the value of L from the given expression. Note that the given problem is simple to solve. We need to make arrangements, so that the terms containing the variable L will be on the left hand side and rest other terms on the right hand side of the equation. Firstly, we will divide the both sides of the equation by a suitable term. Then we cancel out the common terms and simplify the given expression. We solve for the variable L while keeping the equation balanced. Then we obtain the desired result for the given problem.

Complete step-by-step answer:
Given an expression of the form $32\text{LW = V}$ …… (1)
We are asked to solve for L in the above equation (1).
i.e. we need to find the value for the variable L from the given expression.
So we make use of suitable mathematical operations to find the solution in terms of the variable L.
We need to make arrangements, so that the terms containing the variable L 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 L.
Firstly, let us divide both sides of the equation (1) by $32$, we get,
$\Rightarrow {\displaystyle \frac{32\text{LW}}{32}}={\displaystyle \frac{\text{V}}{32}}$
Now we cancel the common factor 32 and rewrite the expression as,
$\Rightarrow \text{LW = }{\displaystyle \frac{\text{V}}{32}}$ …… (2)
Now the variable W is still present on the L.H.S. and we need to isolate it.
So we divide the expression in the equation (2) by W, we get,
$\Rightarrow {\displaystyle \frac{\text{LW}}{\text{W}}}\text{ = }{\displaystyle \frac{\text{V}}{32\text{W}}}$
Cancelling the common factor W and rewriting the expression as,
$\Rightarrow \text{L = }{\displaystyle \frac{\text{V}}{32\text{W}}}$
Hence the required solution for the equation $32\text{LW = V}$ in terms of the variable ‘L’ is given by $\text{L = }{\displaystyle \frac{\text{V}}{32\text{W}}}$.

Note:
If the equation satisfies the expression of ‘L’, 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.