91Ó°ÊÓ

When solving an equation, one of the key steps is isolating the variable you are solving for. This means getting the variable by itself on one side of the equation.
In our example, we need to solve for the variable \( W \) in the formula \( V = \frac{L W T}{144} \). In order to get \( W \) by itself, we need to remove any other variables or constants that are with it.
To start, we should handle the fraction. By multiplying both sides of the equation by 144, we eliminate the fraction and make the equation easier to work with.
After this step, we see that it's necessary to divide by the remaining variables \( L \) and \( T \) to completely isolate \( W \). This way, \( W \) will be all alone on one side of the equation, giving us a clear solution.

Algebraic manipulation involves performing operations to both sides of an equation to maintain equality, while simplifying or rearranging the equation.
In our example, we first identify the formula: \( V = \frac{L W T}{144} \). To start solving for \( W \), we multiply both sides of the equation by 144. This step eliminates the fraction, resulting in: \( 144V = L W T \).
Next, we use division to isolate \( W \). Dividing both sides by \( L T \) simplifies the equation to \( W = \frac{144V}{L T} \). These steps of multiplication and division are key forms of algebraic manipulation that help break down the equation into a more workable form.

Multiplication and division are powerful tools when solving equations. They help us move terms around and simplify expressions.
For the equation \( V = \frac{L W T}{144} \):

• First, we multiply both sides by 144. This step is crucial as it removes the fraction and changes the equation to \( 144V = L W T \).
• Next, we divide both sides by the terms accompanying \( W \), which are \( L \) and \( T \). This isolates \( W \) and gives us the final solution: \( W = \frac{144V}{L T} \).

By using multiplication to eliminate the fraction and division to isolate the variable, we transform the equation in a way that makes it easier to solve. These operations maintain the balance of the equation, ensuring that both sides remain equal.