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To solve a linear equation, the primary goal is to isolate the variable. This means we want to get the variable by itself on one side of the equation. In our example, the equation is
\[x - 6 = -9\]
To start isolating the variable, identify what needs to be removed to leave the variable alone. Here, we need to remove the -6. We do this by performing the opposite operation. Since -6 is subtracted, we add 6 to both sides of the equation:
\[ x - 6 + 6 = -9 + 6 \]
Adding 6 cancels out the -6 on the left side:
\[ x = -3 \]
Now, we have isolated the variable. Always remember, whatever operation you do on one side of the equation, you must do to the other side. This keeps the equation balanced.

After finding a solution, it's crucial to verify it to ensure it's correct. Verification involves substituting the solution back into the original equation. For our equation:
\[ x - 6 = -9 \]
We found that \( x = -3 \). Substitute \( -3 \) back into the equation:
\[ -3 - 6 = -9 \]
Perform the subtraction on the left side:
\[ -9 = -9 \]
Since both sides of the equation are equal, our solution \( x = -3 \) is correct. Always verify your solutions to avoid mistakes and ensure accuracy.

Simplifying equations involves reducing them to their simplest form to isolate the variable. This process makes solving easier and avoids confusion. When simplifying:

• Combine like terms.


• Perform operations logically step-by-step.

In the given equation
\[ x - 6 = -9 \]
There are no like terms to combine, so we only need to add 6 on both sides:
\[ x - 6 + 6 = -9 + 6 \]
Which simplifies to
\[ x = -3 \]
Simplification helps to clearly see the steps you need to isolate the variable. Always simplify as much as you can before solving.