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In solving linear equations, one of the key steps is to isolate the variable. This means getting the variable by itself on one side of the equation. By doing this, you can easily figure out its value. Let's look at our example, where the equation is 9.2n + 6.4 = 43.2.

To isolate the variable term, you need to remove the constant (numbers without variables) from the side containing the variable. Here, we subtract 6.4 from both sides of the equation:
\[9.2n + 6.4 - 6.4 = 43.2 - 6.4\] After simplifying, we get: \[9.2n = 36.8\]

Now, the variable term is isolated, making our job easier. Isolating the variable is essential because it prepares the equation for the next step, allowing us to solve it straightforwardly.

Once the variable term is isolated, it's time to solve the equation. The main goal here is to find the value of the variable. In our example, we have already isolated the variable term:\[9.2n = 36.8\]

To solve for n, we need to get n by itself. We do this by dividing both sides of the equation by 9.2, which is the coefficient (the number in front of the variable):

\[n = \frac{36.8}{9.2}\]
When we perform the division, we get:

\[n = 4\]

Now, we have the solution to our equation. Solving equations involves performing operations that simplify the equation step-by-step until you find the variable's value. Always remember to check your work by plugging the value back into the original equation to ensure it's correct.

Prealgebra is a crucial part of mathematics that lays the foundation for algebra. It involves a lot of basic arithmetic and introduces concepts essential for solving equations. Let's explore the prealgebra steps involved in solving our example equation:

1. **Understanding and Setting Up the Equation**: Start by understanding the components of your equation. In our example, 9.2n + 6.4 = 43.2, we know we need to solve for n.
2. **Isolate the Variable**: We subtract 6.4 from both sides to isolate the term with n:\[9.2n = 36.8\]
3. **Solving for the Variable**: Now divide both sides by 9.2 to solve for n:
\[n = \frac{36.8}{9.2}\]
4. **Simplify**: Simplify the division to find the value of n:\[n = 4\]

These steps form a simple yet powerful process for solving equations. Understanding and mastering these prealgebra steps will set a solid foundation for more complex algebra and other math topics in the future.