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Solving equations involves finding the value of a variable that makes the equation true. In our example, we need to solve the equation \(\frac{-t}{5} = 9\). Here’s the strategy you'll use:

Identify the goal: The goal is to isolate the variable \(t\). To do this, you need to eliminate any fractions, coefficients, and constants on the variable's side of the equation.
Use the multiplication principle: The multiplication principle states that if you multiply or divide both sides of an equation by the same nonzero number, the two sides remain equal.
Simplify the equation step by step: Each step should bring you closer to isolating the variable. Consistently applying basic algebraic rules will help you solve the equation.

Fractions can make equations look complicated, but the key is to eliminate them as soon as possible. Here’s how you can do that using the multiplication principle:

Identify the fraction: In the equation \(\frac{-t}{5} = 9\), the term \(\frac{-t}{5}\) is a fraction with 5 as the denominator.
Multiply by the denominator: Multiply both sides of the equation by 5 to eliminate the fraction. This means you perform the operation: \(\frac{-t}{5} \times 5 = 9 \times 5\).
Simplify: After multiplying, the left side becomes \(-t\), and the right side simplifies to 45, resulting in the equation \(-t = 45\). Now, the equation is much simpler to solve.

Eliminating fractions early in the process can greatly simplify your tasks and reduce the chances of making errors.

After solving an equation, it is crucial to check your solution to ensure it is correct. Here’s how you can do that:

Substitute the solution back into the original equation: Take the value you found for the variable and replace the variable in the original equation with this value. In this case, you found \(t = -45\). Substitute this back into the original equation: \(\frac{-(-45)}{5} = 9\).
Simplify the substituted equation: This simplifies to \(\frac{45}{5} = 9\).
Verify the equality: Ensure that both sides of the equation are equal. Since \(\frac{45}{5} = 9\) is a true statement, your solution \(t = -45\) is correct.
Checking solutions helps to confirm that the steps you followed to solve the equation were correct and that your final answer is accurate.