Problem 53 - Beginning and Intermediate Algebra

Question

Find each absolute value. |-6|

Step-by-Step Solution

Answer

6

Step 1: Understand Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is always non-negative.

Step 2: Identify the Number Inside Absolute Value

In this case, the number inside the absolute value bars is -6.

Step 3: Apply Absolute Value

Since absolute value measures distance, \(-6\) will be converted to its positive equivalent. So, \|-6|\ becomes 6.

Key Concepts

Number Line

The number line is a visual representation of numbers in a straight line.
It includes both negative and positive numbers extending infinitely in both directions.
The zero point is located at the center of this line.

When dealing with absolute values, the number line helps us easily see how far a number is from zero.
For example, the number -6 is located six units to the left of zero.
Positive numbers are to the right of zero, and negative numbers are to the left.

Negative Numbers

Negative numbers are numbers less than zero.
They are usually written with a minus sign in front of them, like -6, -3, and -1.
On a number line, negative numbers are found to the left of zero.
These numbers represent values or quantities that are below a certain point (like sea level) or owing (like debt).

In the context of absolute value, negative numbers are treated as having the same distance from zero as their positive counterparts.
For example, -6 and +6 have the same absolute value of 6 because both are six units away from zero.

Positive Numbers

Positive numbers are numbers greater than zero.
They are written without any sign or with a plus sign in front, like 3, +5, and 7.
Positive numbers are located to the right of zero on a number line.
These numbers represent values or quantities greater than zero, often used to indicate gains or elevations above a certain point.

In the realm of absolute value, positive numbers remain unchanged.
The absolute value of any positive number is simply the number itself. For instance, the absolute value of +6 is 6.

Distance from Zero

Absolute value measures how far a number is from zero on the number line.
This measure, or distance, is always non-negative.
Whether a number is positive or negative, its distance from zero does not change.

For instance, \(-6\) is 6 units away from zero. Therefore, \|-6\| = 6.
Similarly, 6 is also 6 units away from zero, so \|6\| = 6.

Understanding absolute value as the distance from zero helps simplify problems and makes the concept easier to grasp.