91Ó°ÊÓ

One of the key steps to solve equations in algebra is isolating the variable. This means making sure that the variable (like our 't' in the equation) is by itself on one side of the equation.

For example, in the equation \(0.2t = 8\), our goal is to get 't' alone.

To isolate 't,' we need to undo whatever is being done to it. Here, 't' is being multiplied by 0.2. The opposite operation of multiplication is division.

So, to undo the multiplication by 0.2, we divide both sides of the equation by 0.2. This gives us:

\[\frac{0.2t}{0.2} = \frac{8}{0.2}\ \]

When we simplify this, we get \(t = 40\). This process of isolating the variable helps us find the solution.

Remember, what you do to one side of the equation, you must do to the other side. This keeps the equation balanced.

After solving an equation, it's essential to verify the solution. This step confirms that the solution works within the original equation.

For our example, we found that \(t = 40\). Now, we need to check if this value of 't' really satisfies the original equation \(0.2t = 8\).

To verify, substitute 't' with 40 in the original equation:

\0.2 \times 40 = 8\.

When we perform the multiplication, we get:
\8 = 8\.

Since both sides are equal, our solution is correct.

Verification helps to catch any mistakes made during the calculation process and ensures the solution is accurate.

This final step is often overlooked, but it’s crucial for confirming the accuracy of your answer. Always make it a habit to verify your solutions.