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Chapter 1: Problem 88

Simplify. \(-|8|\)

Short Answer

Expert verified
-8

Step by step solution

01

Understanding Absolute Value

The absolute value of a number is its distance from zero on the number line, which is always a non-negative number. For any positive number such as 8, its absolute value is the number itself. Hence, \(|8| = 8\).
02

Applying Negation to Absolute Value

Now, we need to apply negation to the absolute value we have just calculated. The problem is \(-|8|\), so we need to find the negation of \(8\). Negating \(8\) gives us \(-8\).

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Key Concepts

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

Number Line
The number line is a visual representation of integers laid out in a straight line. Each point on this line corresponds to a number, making it easy to visualize concepts like absolute value and distance.

To understand the absolute value, imagine standing at zero on the number line and walking to reach a particular point, like 8. Your steps, regardless of direction, represent the absolute value.
  • Numbers to the right of zero are positive.
  • Numbers to the left are negative.
The absolute value, such as \(|8| = 8\), signifies how many units a number is from zero, ignoring direction.
Negation
Negation involves reversing the sign of a number. It's like taking a number and flipping it across zero on the number line. If you start with a positive number like 8, negation turns it into -8.

When you negate an absolute value, you apply this flip to the distance calculated:
  • Start with the absolute value, such as \(|8| = 8\).
  • Apply negation: \(-|8| = -8\).
This simple flip shows how negation impacts the direction on the number line, converting positive steps into negative ones.
Distance from Zero
Distance from zero is one of the foundational ideas in understanding absolute value. It asks how far a number is from zero on the number line, without worrying about direction.

Think of it as measuring the length between two points, where zero is always one point:
  • The distance for positive 8 is simply 8.
  • The same goes for negative 8, since absolute value ignores direction.
Thus, the absolute value \(|8|\) represents this distance, always resulting in a non-negative number.

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