91Ó°ÊÓ

First, we need to get all the variable terms on one side of the equation and the constant terms on the other.
In our example, we have the equation:
2x = 5 + 7x
To isolate the variable, we must move all terms containing 'x' to one side. This makes solving the equation easier.

This is done by moving the 7x term to the left side. We do this by subtracting 7x from both sides of the equation:
\[ 2x - 7x = 5 + 7x - 7x \]
Notice that when you subtract something from one side, you must do it on the other side as well. This keeps the equation balanced.

After subtraction, we simplify:
\[ -5x = 5 \]
Now the variable 'x' is isolated with its coefficient on one side of the equation, making it easier to solve.

Subtracting terms is a crucial step in solving linear equations. In our example:
\[ 2x - 7x = 5 + 7x - 7x \]
We subtracted 7x from both sides. But why?

To isolate the variable 'x', we need to get all terms with 'x' on the same side of the equation. By subtracting 7x:
- We removed 7x from the right side.
- We moved it to the left side.

Subtracting terms should be done in a balanced way.
This means making sure you perform the same operation on both sides of the equation. This balancing act helps maintain equality.
Think of an equation as a balanced scale: what happens on one side must happen on the other to keep it level.

Once the variable is isolated, we often need to divide to solve the equation completely.
From our simplified equation:
\[ -5x = 5 \]
We need to isolate 'x'.
The coefficient of 'x' here is -5. To get 'x' by itself, divide both sides of the equation by -5:
\[ x = \frac{5}{-5} \]
This step gives us:
\[ x = -1 \]
Dividing is a straightforward step but important. It helps us find the exact value of the variable.
Remember:
- Always divide both sides by the same number
- Ensure you follow sign rules for division (positive/negative).

After division, you've solved for 'x'. In this case, 'x' equals -1.