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To solve linear equations effectively, you need to isolate the variable you're solving for. This means getting that variable by itself on one side of the equation.
In our example, the goal is to solve for \(A\) in the equation \(2000A + 4500B = 18,000\).
The first step is to remove the term involving \(B\) from the left side. We do this by subtracting \(4500B\) from both sides, like this:
\(2000A + 4500B - 4500B = 18,000 - 4500B\), which simplifies to \(2000A = 18,000 - 4500B\).
Now, \(A\) is on its own on one side, making the next steps more straightforward. Remember, each operation you do to one side of the equation must also be done to the other side. This keeps the equation balanced and helps you get \(A\) by itself.

Simplifying expressions is a crucial step in solving linear equations. After isolating \(A\) in \(2000A = 18,000 - 4500B\), we must simplify it further if possible.
The simplified form will make the calculation easier and clearer.
Here, our next step is to divide both sides by 2000 to isolate \(A\). We get:
\(A = \frac{18,000 - 4500B}{2000}\).
This form is better, but we can simplify even more. We divide both terms on the right-hand side by 2000 individually:
\(A = \frac{18,000}{2000} - \frac{4500B}{2000}\).
Solving these fractions gives us a further simplified equation:
\(A = 9 - 2.25B\).
This is a cleaner and more understandable form of the equation.

Solving for a specific variable means isolating it and simplifying the equation so you have that variable alone on one side. In solving \(2000A + 4500B = 18,000\) for \(A\), we started by isolating \(A\) and simplifying the expression.
Finally, we solved for \(A\) and got the simplified result:
\(A = 9 - 2.25B\).
This final form is the solution to our problem, giving us \(A\) in terms of \(B\) in the simplest way possible.
Steps to remember:

• Remove other terms from the side of your target variable.
• Perform operations to isolate the variable fully.
• Simplify the equation step by step for clarity.

With practice, these steps become natural, making solving linear equations much easier.