91Ó°ÊÓ

Variable isolation is a fundamental concept in algebra. It involves manipulating an equation to get a specific variable by itself on one side of the equation. In the given exercise, our goal is to isolate the variable \(R\) in the formula \(I = \frac{k E}{R}\). This means we need to perform operations that will leave \(R\) alone on one side of the equation.

To start, identify the term containing \(R\). Here, \(R\) is in the denominator on the right side of the equation. Moving \(R\) out of the denominator is crucial to isolate it. We can achieve this by multiplying both sides of the equation by \(R\), which will remove \(R\) from the denominator. Remember, whatever operation you perform on one side of the equation, you must also do on the other side to maintain balance. So, we perform the multiplication as follows:

\[IR = kE\]

At this point, \(R\) is no longer in the denominator, making it easier to isolate.

Multiplication in algebra is used to balance equations, especially when dealing with fractions or multiple terms. In the context of solving equations, it's an essential tool for getting rid of denominators.

In our example, to eliminate the fraction, we multiplied both sides of the equation \(I = \frac{k E}{R}\) by \(R\). This operation is strategic, as it simplifies the equation by removing \(R\) from the denominator and balancing both sides. After this multiplication, we have:

\[IR = kE\]

Now, the variable \(R\) is part of a product on the left side of the equation, which makes it more manageable to isolate in further steps.

Division is another key operation used in solving equations. When a variable is part of a product, division helps to isolate the variable by 'undoing' the multiplication.

After we multiplied both sides by \(R\) to get \(IR = kE\), our next step is to isolate \(R\) completely. We do this by dividing both sides of the equation by \(I\), thus:


\[R = \frac{k E}{I}\]

This division effectively isolates \(R\) on the left side, giving us the solution we were looking for. Remember, always perform the same operation on both sides to maintain the equation's balance.

In summary, variable isolation often requires a combination of multiplication and division to solve for the desired variable efficiently.