91Ó°ÊÓ

One of the fundamental skills in algebra is isolating a variable. When you isolate a variable, you are essentially solving for that variable by getting it alone on one side of the equation. This allows you to see its value in terms of the other variables given.
For example, in the equation given in the exercise: \[ d = rt \], our goal is to solve for the variable \(r\). To do this, we need to separate \(r\) from the other elements of the equation.
Begin by identifying the term attached to \(r\). In this case, \(r\) is multiplied by \(t\). Therefore, we need to perform the opposite operation (which is division) to isolate \(r\).
This step-by-step approach can be applied to isolating any variable in an equation.

Understanding division in algebra is crucial for solving equations. Division is used to undo multiplication or to simplify fractions.
In the context of the given exercise, we need to divide both sides of the equation \(d = rt\) by \(t\) to solve for \(r\). This operation looks like this: \[ r = \frac{d}{t} \].
By dividing both sides by \(t\), we effectively cancel out the \(t\) on the right-hand side, leaving \(r\) by itself.
Remember, whatever you do to one side of the equation, you must do to the other. This preserves the equality and ensures your solution is correct.

Rearranging formulas is a common task in algebra. It involves manipulating the equation to make a particular variable the subject.
For the given equation \(d = rt\), we need to rearrange it to solve for \(r\).
Start with the original equation:\[ d = rt \].
Then, we identify the desired subject (\(r\)) and determine the necessary steps to isolate it. In this case, since \(r\) is being multiplied by \(t\), we divide both sides by \(t\):\[ r = \frac{d}{t} \].
This practice can then be extended to more complex equations and allows for a greater understanding of how different variables interact within a formula.