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When working with algebraic expressions, you might come across terms that look different but share a common variable and exponent. For example, in the expression \(x - 0.55x\), you see the terms \(x\) and \(0.55x\) which can be combined because they both involve the variable \(x\) with no exponent, or an implied exponent of 1.

To combine like terms, simply add or subtract the coefficients (the numerical parts) of these terms. Think of the variable part as a container that remains unchanged, while you adjust the amount inside it by adding or subtracting.

Imagine you have 1 apple (\(x\)) and you lose 55% of this apple (\(0.55x\)), how much of the apple do you have left? You would have \(x - 0.55x = (1 - 0.55)x = 0.45x\), which is 45% of the original apple. Combining like terms is a foundational step in simplifying algebraic expressions and forms the basis for more complex operations in algebra.

Subtraction in algebra is very similar to arithmetic subtraction but with one key difference: you also need to consider variables. In the problem \(x - 0.55x\), subtraction is performed between coefficients that are multiplying the same variable.

Here's a simple way to understand algebraic subtraction: you look at the coefficients as portions or pieces of a whole item represented by the variable. If \(x\) represents a whole item, \(0.55x\) is a part of it. Subtracting these pieces means you're taking away a portion from the whole, and you're left with the remainder.

It's crucial to ensure that the variable portions you're subtracting are actually compatible or 'like' (i.e., they represent the same quantity and type). If they are, then it is just a case of subtracting the numbers in front, as you would when dealing with plain numbers, and keeping the variable part intact.

Prealgebra lays the groundwork for understanding the foundational concepts of algebra by introducing basic mathematical operations and their properties. It combines arithmetic with the beginning elements of algebra, which includes working with integers, fractions, and variables like in the problem \(x - 0.55x\).

Prealgebra helps you get comfortable with variables and the idea that they represent unknown quantities. It also teaches how to manipulate and simplify expressions, setting up a solid base for more complex algebraic concepts.

One of the primary goals is to learn how to translate real-world situations into mathematical expressions and then solve them. For instance, if you have a whole and you take away a part, prealgebra teaches you to represent this as an expression like \(x - 0.55x\) and then simplify it to find the remaining part (\(0.45x\). Understanding these basics is essential before moving on to high school algebra where the problems become more abstract and less numerical.