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Understanding how to evaluate expressions is fundamental in algebra. This is the process of determining the value of an algebraic expression by substituting numbers for variables and performing the operations in the correct order. In the given exercise, you are asked to evaluate the absolute value of the expression \(3 - 8\). This involves first conducting the subtraction, which is the sole operation within the absolute value notation.

Here's how you approach it: Calculate \(3 - 8\) to get \-5\. Since this is the only step before considering the absolute value, you conclude the evaluation of the internal expression. The key to evaluation is to carefully perform one step at a time and follow the order of operations, which in this example is simplified to a single subtraction.

The concept of subtraction is well-known as a method for finding the difference between two numbers. When you subtract a larger number from a smaller number, like in the exercise \(3 - 8\), the result is a negative number. This is because you are essentially determining how much less 3 is than 8. It's important to recognize that in everyday language, we might say that 3 is 5 less than 8, but in mathematical terms, we express this as \(3 - 8 = -5\).

Subtraction is a fundamental operation that underlies more complex concepts in mathematics. It's intrinsic to understanding algebra, calculus, and beyond. So, it's important to be comfortable with negative results when they occur, as they are just as valid as positive ones in the world of mathematics.

The absolute value properties are crucial when evaluating expressions containing absolute value notations. One key property to remember is that the absolute value of a number, such as \(|-5|\), represents the distance of that number from zero on a number line. This implies that the absolute value is always non-negative, as distance cannot be negative.

For the provided exercise, after finding that the subtraction resulted in \-5\, you apply this property to determine that the absolute value of \-5\ is 5, written mathematically as \(|-5| = 5\). Regardless of whether the number inside the absolute value is positive or negative, the outcome is the same since you're looking at how far away the number is from zero. Recognizing this property clarifies why \(|-5|\) and \(|5|\) both evaluate to 5, and it emphasizes the non-directional nature of absolute values in measuring distance.