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When solving linear equations, one of the first steps is to isolate the variable. Isolating the variable means getting the variable (*t* in this case) alone on one side of the equation. This helps us understand what value the variable represents.

To do this, you need to move all other numbers or terms to the other side of the equation.

For example, in the equation

\( 50 = 5 \cdot \ t \),

we want to isolate t. This means we need to get rid of the 5 that is multiplied by t, so t is alone on one side of the '=' sign.

Remember, isolating the variable is a crucial step in many types of algebra problems, not just linear equations.

Once we've decided to isolate our variable, sometimes we need to use division to do so. In our example, we have:

\( 50 = 5 \cdot \ t \)

To isolate t, we need to remove the 5 that is multiplying t. We do this by dividing both sides of the equation by 5. Division in algebra follows the Golden Rule: Whatever you do to one side of the equation, you must do to the other side too. This helps to keep the equation balanced.

So when we divide both sides by 5, we get:

\( \frac{50}{5}= \frac{5\cdot t}{5} \)

This simplifies to:

\( 10= t \)

Division in algebra is a powerful tool for isolating variables. Always remember to divide all terms on both sides of the equation to keep things balanced.

The final step in solving linear equations is simplification. This means breaking down the equation into its simplest form so we can solve it easily.

In our example, after dividing both sides by 5, our equation became:

\( \frac{50}{5}= \frac{5 \cdot t}{5} \)

We simplified this to:

\( 10= t \)

Here, 50 divided by 5 gives 10, and \( \frac{5 \cdot t}{5} \) simplifies to just t, because 5 divided by 5 is 1. So we have:

\( 10= t \).

Notice how we simplified both sides to get the simplest form of the variable t. Simplification makes it about finding an easily understandable value for the variable. Always check through your steps to ensure the equation is balanced and simplified accurately.