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The concept of isolating the variable is crucial when solving linear equations. It means to get the variable you are solving for by itself on one side of the equation. Let's take the example given in the exercise:

You start with the equation \( -2.7u = -9.72 \). In this case, our variable is \( u \). To isolate \( u \), we aim to remove the coefficient (number in front) attached to \( u \) on the left side of the equation. The coefficient here is -2.7.

To isolate \( u \), we divide both sides of the equation by -2.7. This operation maintains the balance of the equation, leaving us with: \[ u = \frac{-9.72}{-2.7} \]. By performing this division, you successfully isolate the variable. Now, it's easy to solve for \( u \).

Division is a fundamental operation in algebra, particularly when solving equations. By dividing both sides of an equation by the same number, you maintain the equality, making it a reliable method for isolating variables.

In the example \( -2.7u = -9.72 \), we need to divide both sides by -2.7 to isolate \( u \). Why? Because -2.7 is the coefficient of \( u \). Here’s how you do it:

• \( -2.7u \div -2.7 = u \)
• \( -9.72 \div -2.7 = 3.6 \)

This division tells us that \( u \) is equal to 3.6.

Remember, whatever you do to one side of the equation, you must do to the other. This keeps the equation balanced and helps you find the correct solution.

Prealgebra is all about building a strong mathematical foundation. Key concepts include basic operations, fractions, and solving simple equations. To solve equations like \( -2.7u = -9.72 \), follow these steps:

• Understand the problem: Identify what you need to find. Here, it's the variable \( u \).
• Isolate the variable: Use operations like division to get the variable by itself on one side of the equation.
• Perform the arithmetic: Calculate the division to find the value of the variable. For example, \( \frac{-9.72}{-2.7} = 3.6 \).

By focusing on these steps, you can tackle many prealgebra problems with confidence. Practice makes perfect, so work through several examples to strengthen your problem-solving skills.