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When solving linear equations, the first step often involves identifying and combining like terms. Like terms are terms in an equation that have the same variable raised to the same power. For instance, in the equation \(3x + 5x = 10\), both \(3x\) and \(5x\) are like terms because they both contain the variable \(x\). By adding these together, you simplify the equation to \(8x = 10\). Simplification by combining like terms makes it easier to solve the equation.

However, not all equations have obvious like terms. In the equation \(1 - 8 = n + 2\), we see numbers but no like terms to combine. This means we'll move on to the next step without simplifying.

The goal of solving an equation is to find the value of the unknown variable. To do this, we need to get the variable by itself on one side of the equation, which is known as isolating the variable.

In our example, \(1 - 8 = n + 2\), the variable \(n\) is on the right side of the equation. We can isolate \(n\) by eliminating the constant \(+2\) from the right side. This is done by performing the opposite arithmetic operation—in this case, subtraction—on both sides of the equation: \(1 - 8 - 2 = n + 2 - 2\).

Simplifying this gives \(-9 = n\). With \(n\) isolated, we have found our solution. With practice, moving terms across the equation gets easier as you become familiar with opposite operations.

Once we have a potential solution for the variable, it is important to check that it satisfies the original equation. This step is called validating the solution.

For our equation \(1 - 8 = n + 2\), we found \(n = -9\). To validate this solution, substitute \(-9\) back into the original equation, replacing \(n\): \(1 - 8 = -9 + 2\). Simplifying both sides yields \(-7 = -7\).

Since both sides of the equation match after substitution, our solution is correct. Validating your solution helps ensure accuracy and builds confidence in your results. It's an important habit that checks your work and verifies that you've solved the equation properly.