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An essential step when solving linear equations is the isolation of the variable. In this context, isolating the variable refers to getting the variable by itself on one side of the equation, with all other terms moved to the opposite side. This helps in identifying the variable’s value.
To isolate the variable, you should first eliminate any coefficients or other terms associated with it. In the example equation, \[ 10.8t = -9.072, \]our task is to isolate the variable \( t \). To do this, we have to eliminate the coefficient \( 10.8 \) attached to \( t \) by using a division operation.

• Begin by identifying the coefficient. Here, it is \( 10.8 \).
• Divide both sides of the equation by this coefficient to isolate \( t \).

By performing these steps, we draw closer to finding out what \( t \) equals.

Once we have decided to use division to isolate the variable, it's crucial to understand how division operations work in this context. In mathematics, division allows us to simplify expressions by making the number on each side of an equation smaller by a specific factor.
In the equation \( 10.8t = -9.072 \), dividing each side by \( 10.8 \) yields:\[\frac{10.8t}{10.8} = \frac{-9.072}{10.8}.\]This simplifies the equation by effectively removing the \( 10.8 \) coefficient from \( t \), as the division of any number by itself equals 1, meaning:

• \( \frac{10.8}{10.8} = 1 \)
• Thus,\( 10.8t \div 10.8 = t \)

You're left with:\[t = -\frac{9.072}{10.8}.\]Performing the division operation simplifies further to find the value of \( t \), which, in this case, is \( -0.84 \).

Verifying your solution after solving an equation is a critical part of the process, ensuring the calculated value is correct. The verification process confirms if your answer satisfies the original equation.
To check if \( t = -0.84 \) is indeed the right answer, you should substitute \( t \) back into the original equation:\[10.8(-0.84) = -9.072.\]Calculate the left side of the equation:

• Multiply \( 10.8 \) by \(-0.84 \), yielding \(-9.072 \).

If both sides of the equation are equal, this means the solution is correct:\[-9.072 = -9.072.\]Here, the left side equals the right side, confirming our solution \( t = -0.84 \) is accurate. Remember, checking your solution is a fantastic way to double-check your work and prevent mistakes.