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Understanding how to isolate the variable is the first step to solving linear equations. This means getting the variable (often represented as x, y, or another letter) alone on one side of the equation. To do this, you might need to use operations such as addition, subtraction, multiplication, or division.

For the exercise given: \(x - 9 = 8\), the variable is x, and our goal is to get x by itself. Since x is currently being subtracted by 9, we need to do the opposite operation to both sides of the equation, which is adding 9.

The equation changes to:
\[x - 9 + 9 = 8 + 9\]
Simplifying both sides of the equation now shows:
\[x = 17\]
By isolating x, we've moved forward to find our solution.

Once we isolate the variable, the next step is simplifying the equation. Simplifying makes the equation easier to understand and solves the problem.

In our example, after adding 9 to both sides, we have \[x = 17\]. There are no further simplifications needed here, as the variable x is already isolated and equates to 17.

But not all equations will be this straightforward. In other scenarios, you might need to:

• Combine like terms
• Divide or multiply both sides by a number
• Distribute a number across terms inside parentheses

Simplifying ensures that you accurately solve for the variable in question.

After isolating the variable and simplifying the equation, it's essential to check your solution. This step ensures that your solution is correct and that no mistakes were made during the process.

To check our solution in the provided exercise, we substitute x back into the original equation:
\[x - 9 = 8\]
Now, replace x with 17 (our solution):
\[17 - 9 = 8\]
Simplify and verify:
\[8 = 8 \]
Since both sides of the equation are equal, our solution x = 17 is indeed correct.

Always remember to check your solutions as this step confirms the accuracy of your work and helps you develop a thorough understanding.