91Ó°ÊÓ

When solving linear equations, one of the most crucial steps is to isolate the variable. This means we want to get the variable (often represented by letters like x or y) alone on one side of the equation.
For example, given the problem: \[8 = 5x - 3\], let's focus on isolating x.
Here, we need to remove the constants and coefficients associated with x.
The goal is to manipulate the equation to have x all by itself.
In our exercise, we start by eliminating the -3 on the right side. We do this by adding 3 to both sides:
\[8 + 3 = 5x - 3 + 3\]
This brings us to:
\[11 = 5x\]
Notice how we performed the same operation (adding 3) on both sides of the equation. This keeps the equation balanced, which is essential to maintain equality.

Once we have isolated the variable on one side of the equation, we proceed to solve for the variable.
This step involves undoing any multiplication or division to get the variable by itself.
In our example, we have:
\[11 = 5x\]
Here, x is multiplied by 5. We need to divide both sides of the equation by 5 to solve for x:
\[x = \frac{11}{5}\]

By dividing both sides by the coefficient of x (which is 5), we achieve our goal of solving for x.
The final result is:
\[x = 2.2\]Using this method, x is now isolated, and we have found its value.

Basic algebra involves understanding and manipulating variables, coefficients, and constants in equations. It's the foundation for solving linear equations like the one in our example.
Key concepts to remember in basic algebra include:

• **Variables**: Symbols (often letters) that represent unknown values.
• **Constants**: Known values that do not change.
• **Coefficients**: Numbers multiplied by the variables.

In our exercise:
\[8 = 5x - 3\]
8 is a constant, 5 is the coefficient, and x is the variable.
Understand that equations are like balances: whatever you do to one side, you must do to the other to keep it balanced.
This principle helps us isolate and solve for variables effectively.