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Chapter 1: Problem 55

Find each absolute value. \(-|12|\)

Short Answer

Expert verified
-12

Step by step solution

01

Find the Absolute Value

The absolute value of a number is its distance from 0 on the number line, regardless of direction. Therefore, the absolute value of 12 is \(|12| = 12\).
02

Apply the Negative Sign

In this problem, the absolute value is inside a negative sign. So after finding the absolute value, the next step is to apply the negative sign to it: \(-|12| = -12\).

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Key Concepts

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

absolute value
The absolute value of a number tells us how far that number is from zero on the number line. It doesn't care about the direction. This means both 12 and -12 have the same absolute value, which is 12.

To show the absolute value in a mathematical expression, we use vertical bars around the number. For example, the absolute value of -12 is written as \(|-12| = 12\). When solving for absolute values, you just need to consider how far the number is from zero and ignore whether it's positive or negative.

Here are some key points about absolute values:
  • The absolute value is always non-negative.
  • It represents the 'distance' a number is from zero.
  • Operators inside the absolute value bars are first evaluated before taking the absolute value.
By understanding these points, you can tackle absolute value problems with confidence.
negative sign
In mathematics, a negative sign places emphasis on the direction of a number. When you see a negative sign, it means the number is in the opposite direction from the positive number on the number line.

When dealing with absolute values and negative signs, it's important to understand the order of operations. For example, in the expression \-|12|, you first find the absolute value of 12, which is 12, and then apply the negative sign. This gives \(|-12|\).

So, the steps are:
  • Find the absolute value of the number inside the absolute value bars.
  • Apply the negative sign if it's in front of the absolute value bars.
These steps ensure you get the correct final answer while adhering to the right order of operations.
distance from zero
When we talk about the 'distance from zero' in math, we refer to how far a number is from zero on the number line. This concept is essential in understanding absolute values.

The distance from zero is always a positive number. For example, both 12 and -12 are 12 units away from zero. This is why their absolute values are the same: \(|12| = 12\) and \(|-12| = 12\).

By visualizing a number line, you can more intuitively grasp this concept:
  • All points to the right of zero are positive and move away from zero.
  • All points to the left of zero are negative but also move away from zero.
Understanding this helps you solve problems involving absolute values correctly, giving you a clear picture of what 'distance from zero' really means.

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Most popular questions from this chapter

Use the distributive property to rewrite each expression. $$ -\frac{1}{3}(9 x+5) $$

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