91Ó°ÊÓ

The Addition Principle is a fundamental rule in solving linear equations.
It states that you can add (or subtract) the same value to both sides of an equation without changing the equation's equality.
Here, our goal is to keep the balance between both sides while we isolate the variable.

For example, let's start with the initial equation:
\[ x + 3 = 7 \]
According to the addition principle, if we subtract 3 from both sides, the equation remains balanced:
\[ x + 3 - 3 = 7 - 3 \]
This simplifies to:
\[ x = 4 \]
In this case, we used subtraction, which is essentially adding the negative value of 3.
By applying the addition principle, we ensure that both sides of the equation remain equal, helping us find the correct value of the variable.

Isolating the variable is crucial for solving any equation. In our problem, the variable is x, and we aim to have x alone on one side of the equation.
To isolate x in the equation:
\[ x + 3 = 7 \]
We need to remove the number 3 that is added to x.
This is done by subtracting 3 from both sides:
\[ x + 3 - 3 = 7 - 3 \]
After performing the calculation, we get:
\[ x = 4 \]
Now x is by itself, and we have successfully isolated the variable.

This technique helps to simplify the equation and make it easier to see the value of the variable.

Verifying solutions is the final step to ensure your answer is correct.
After finding a solution, it is important to substitute it back into the original equation to check its validity.

For our exercise, we found that:
\[ x = 4 \]
To verify this, substitute 4 back into the original equation:
\[ 4 + 3 = 7 \]
Since both sides of the equation are equal, we confirm that our solution is correct.

This step helps catch any possible errors made during calculations.
Always remember to verify your solutions to ensure the accuracy of your work.