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When solving linear equations, isolating the variable is an essential step. It involves rearranging the equation to get the variable by itself on one side of the equation. This means gathering all terms involving the variable to one side while moving constant terms to the opposite side.

Let's look at the equation you are working with: \(29.5 = 55.1 - 2s\). To start isolating the variable, in this case, \(s\), you want to get rid of the constant \(55.1\) on the variable's side. By subtracting \(55.1\) from both sides, you actively eliminate it, thus isolating the term \(-2s\) on one side.

This transformation brings us to a simpler equation where the only remaining task is to focus on getting \(s\) by itself, leading you closer to your final answer.

Once you've isolated the terms that involve the variable, the next step is to simplify the equation. Simplification makes the equation easier to manage and solve. It involves performing arithmetic operations to consolidate numbers or expressions.

Consider your simplified equation: \(29.5 - 55.1 = -2s\). Here, subtract \(55.1\) from \(29.5\) to simplify the left side of the equation. This gives you \(-25.6\), effectively reducing a complex problem into a simpler one, \(-25.6 = -2s\).

By simplifying correctly, your equation becomes tidier, making the next step—a clean division to solve for the variable—a breeze.

Performing arithmetic operations accurately is key to solving equations correctly. These operations include addition, subtraction, multiplication, and division. Often, they involve negative numbers, so extra care is needed to ensure error-free calculations.

To find the value of \(s\) in the equation \(-25.6 = -2s\), you perform a division. Divide both sides by \(-2\) to isolate \(s\) further, which looks like this: \(s = \frac{-25.6}{-2}\). Upon division, the negative signs cancel each other out, simplifying to \(s = 12.8\).

Remember, arithmetic is the backbone of not just executing solutions but also verifying them. Always double-check your calculations to ensure that your solutions are precise and reliable.