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Chapter 2: Problem 33

Simplify. $$ |-8| $$

Short Answer

Expert verified
The simplified result is 8.

Step by step solution

01

Understand Absolute Value

The first step in simplifying \(|-8|\) is to understand that the absolute value of a number is its non-negative value. Absolute value represents the distance of a number from zero on the number line, regardless of direction.
02

Apply Absolute Value to -8

The absolute value symbol \(|-8|\) tells us to take the non-negative value of -8. Since -8 is 8 units away from zero, it corresponds to the positive number 8.
03

Write the Simplified Result

Therefore, the simplified form of \(|-8|\) is 8. The expression \(|-8|\) simply becomes 8 because absolute value removes the negative sign from the number.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Number Line
A number line is a visual representation of numbers arranged in order, typically on a straight horizontal line. It includes both positive and negative numbers, with zero positioned at the center.
The number line extends infinitely in both directions.
The right side of the number line represents positive numbers, while the left side represents negative numbers.
  • Zero is often called the 'origin' of the number line.
  • This visual tool helps us understand numerical relationships and operations, like addition, subtraction, and absolute values.
A number line is especially useful for understanding absolute value because it allows us to see a number's distance from zero, which is a key principle in calculating absolute values.
Negative Value
Negative values are numbers less than zero, shown on the left side of the number line. Negative numbers are essential in mathematics because they represent quantities below a baseline, like below zero temperature or a debt in finance.

For example:
  • -8 is a negative value and is found to the left of zero on the number line.
  • Negative values might seem small, but they are vital for expressing a range of real-world situations.
When considering the absolute value, a negative becomes positive since absolute value measures distance rather than value.
Distance from Zero
The concept of 'distance from zero' explains the heart of absolute value. Distance from zero refers to how far a number is from zero on the number line, without considering direction. This is why the absolute value of both -8 and 8 is the same; they are both 8 units away from zero.

Key points include:
  • Distance is always a non-negative number, as it indicates "how many" spaces on the number line, not "which direction".
  • This concept is useful for comparisons in mathematics and can be applied to real-life situations where only the quantity of a change matters, not the direction.
Understanding this helps solve problems involving absolute values as it simplifies understanding that \(|-8| = 8\).

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Most popular questions from this chapter

Evaluate. $$ -|x| \text { if } x=-8 $$

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Evaluate: \(\quad-(-|-8|)\)

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