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When it comes to solving linear equations, the goal is to find the value of the unknown variable. The technique known as 'isolating the variable' is used to move the variable to one side of the equation and the constant terms to the other. This is generally done using basic arithmetic operations: addition, subtraction, multiplication, or division.

For instance, in the equation \( n - 5 = -2 \), 'n' is the variable we want to isolate. To do this, we need to get rid of the '-5' that's attached to 'n'. We achieve this balance by performing the same operation on both sides, to maintain the equality. So, by adding 5 to each side, we balance the equation and succeed in isolating 'n' on one side, which is the crucial first step in finding our solution.

Once you have isolated the variable, the next step is to 'simplify the equation.' This involves performing any operations required to solve for the isolated variable. Generally, simplification makes the equation more straightforward and easier to understand.

In our example, we have the equation \( n = -2 + 5 \) after isolating 'n'. To simplify, we perform the addition on the right side. It's akin to tidying up: combining like terms or calculating the results of arithmetic operations. In this case, \( -2 + 5 \) simplifies to 3, leaving us with \( n = 3 \). Thus, simplification brings us one step closer to the answer by revealing the value of 'n'.

After finding what we believe to be the solution to our equation, it's essential to 'check the solution'. This verification step ensures that our found value for the variable actually satisfies the original equation.

Here, we substitute '3' back into the original equation in place of 'n' to get \( 3 - 5 = -2 \). When we simplify this, it gives us \( -2 = -2 \), which is an accurate statement. This confirms that our solution \( n = 3 \) is correct. By checking the solution, we reassure ourselves that no mistakes were made during the process and that the answer is indeed valid within the context of the original problem.