91Ó°ÊÓ

When solving linear equations, one of the first steps is to isolate the variable. This means getting the variable, such as \( x \), by itself on one side of the equation. To do this, you need to perform operations that will leave \( x \) alone.

In our example, we have the equation \( 0.9 x = 18 \). To isolate \( x \), you should divide both sides of the equation by 0.9. This operation simplifies the equation, making it easier to find the value of \( x \). Here’s how it looks:

\[ x = \frac{18}{0.9} \]
By dividing both sides by 0.9, we successfully isolate the variable.

Remember, the purpose of isolating the variable is to simplify the equation so you can easily determine the value of the variable. It’s an essential step in solving linear equations.

Once you have isolated the variable by setting up the equation \( x = \frac{18}{0.9} \), the next step is to perform the division. This means calculating what \( \frac{18}{0.9} \) equals.

To do this division, you can rewrite the equation:

\[ x = \frac{18}{0.9} = \frac{18 \times 10}{0.9 \times 10} = \frac{180}{9} \]
When you simplify \( \frac{180}{9} \), you get: \( x = 20 \).

After performing this division, you find that \( x = 20 \). This division step is crucial because it transforms the equation into a form where the value of the variable becomes apparent.

Remember, always perform the same operation on both sides of an equation to maintain equality. When dividing, make sure your division is accurate to ensure the correctness of the solution.

The final step after solving the equation is to check your solution. This ensures that your answer is correct and satisfies the original equation.

To check the solution, substitute \( x = 20 \) back into the original equation \( 0.9 x = 18 \). Here’s how you do it:

First, substitute the value of \( x \):

\[ 0.9 \times 20 = 18 \]
When you multiply \( 0.9 \) by \( 20 \), you get \( 18 \), which is equal to the right side of the original equation. This confirms that \( x = 20 \) is the correct solution.

Checking your solution is an important practice. It helps you verify that your steps and calculations were done correctly. Always make this a part of your routine when solving equations. By doing so, you'll catch potential mistakes and ensure your answer is valid and accurate.