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Chapter 0: Problem 50

Find each absolute value and simplify if needed. $$ -|-6| $$

Short Answer

Expert verified
-6

Step by step solution

01

- Identify the absolute value

First, identify the absolute value in the expression. In this case, the absolute value is \(|-6|\).
02

- Calculate the absolute value

Calculate the absolute value of -6. The absolute value of any number is its distance from zero on the number line, regardless of direction. Thus, \(|-6| = 6|\).
03

- Apply the negative sign

Now, apply the negative sign that is outside the absolute value to the result obtained in Step 2. Thus, \(-|6| = -6|\).

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Key Concepts

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

absolute value
In algebra, the absolute value of a number refers to its distance from zero on the number line, regardless of the direction. This means we simply take the positive version of any number. For example, the absolute value of -6 and +6 is the same, which is 6. The notation for absolute value involves vertical bars around the number, like this: \(|-6|\). Understanding absolute value is crucial because it helps in simplifying expressions and solving equations that involve distances.
number line
The number line is a visual representation of all real numbers in a straight line, where each point corresponds to a number. Zero is typically marked in the center, with positive numbers to the right and negative numbers to the left. When we talk about absolute value, we consider the distance of a number from zero on this number line. For instance, both -6 and 6 are six units away from zero, even though they are on opposite sides. This visualization helps understand why \(|-6| = 6\). Using a number line can make it easier to grasp the concept of absolute values by seeing the distances directly.
negative sign in algebra
In algebra, a negative sign indicates that a number is less than zero. When dealing with absolute values, a negative sign outside the absolute value bars affects the final result. Let's take the example from the exercise. You start with \(-| -6 |\). First, calculate \(| -6 |\) which is 6. Then, apply the negative sign in front, giving you \(-6\). This shows that while the absolute value makes everything positive, any external negative sign will flip the result back to negative. Understanding how to handle negative signs with absolute values is key in algebra to avoid mistakes in calculations.

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