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When solving linear equations, isolating the variable is one of the first critical steps needed to reach a solution. In simple terms, it means getting the variable by itself on one side of the equation. By doing this, we can clearly see what the variable equals. To begin isolating the variable, identify any constant numbers that are on the same side as the variable. Move these constants to the opposite side of the equation.

For the equation \(-5t + 8 = 18\), the constant is 8. We move 8 to the other side by subtracting it from both sides, leading to \(-5t + 8 - 8 = 18 - 8\). As a result, the equation simplifies to \(-5t = 10\). Now, the variable term \(-5t\) is isolated.

Simplification is a step in solving equations where we combine like terms or reduce both sides of the equation to their simplest forms. This process not only makes the equation easier to handle but also helps in managing errors. In the context of our example \(-5t + 8 = 18\), the simplification occurred right after subtracting 8 from both sides: \[-5t + 8 - 8 = 18 - 8\]. Once the equation was adjusted to \(-5t = 10\), no further simplification of like terms was necessary, so we could proceed to solve for the variable. At this point, it's crucial to ensure both sides of the equation are as simple as possible, removing any brackets if applicable, and preparing for any necessary division or multiplication.

After isolating the variable and simplifying the equation, the next step is to solve for the variable. The objective is straightforward: find the value of the variable that makes the equation true. With the equation \(-5t = 10\), we aim to get \(t\) by itself. Divide both sides by the coefficient of \(t\), which in this case is \(-5\): \[\frac{-5t}{-5} = \frac{10}{-5}\]Performing this division gives \(t = -2\). This solution tells us that the variable \(t\) is equal to \(-2\). It's important to check the solution by plugging it back into the original equation to verify that it satisfies the equation.