Problem 75 - Intermediate Algebra

Question

Find the value of each expression. $$ |20| $$

Step-by-Step Solution

Answer

The value of \(|20|\) is 20.

Step 1: Understanding Absolute Value

Absolute value refers to the distance of a number from zero on the number line, regardless of direction. It's always non-negative.

Step 2: Identify the Number

The number given in this expression is 20. We need to find the absolute value of this number.

Step 3: Apply Absolute Value Definition

Since 20 is positive, according to the definition, its absolute value is itself, i.e., 20.

Key Concepts

Understanding the Number Line

The number line is a simple yet powerful tool in math. It is a straight line with numbers placed at intervals along its length.
It extends infinitely in both directions, with zero in the center, negative numbers on the left, and positive numbers on the right. This line helps us visualize the concept of absolute value easily.
For example, when you look at number 20 on the number line, you can count the units it is from zero. These units represent the distance, which is key to understanding absolute value. Using the number line, you can see that moving to 20 means counting 20 units from zero.

• The number line is continuous; it doesn't stop at whole numbers but includes decimals and fractions.
• Every position on the number line corresponds to a number, defining its positive or negative nature.

Identifying Positive Numbers

In mathematics, positive numbers are all the numbers greater than zero. They appear to the right of zero on the number line. Positive numbers are straightforward: they increase in value as you move to the right.
Being familiar with positive numbers is important when evaluating absolute values. In our exercise, the number is 20, a positive number. Positive numbers can simply be written with their numeric value, without any signs.

• Examples of positive numbers are 1, 5, 20, 100, etc.
• There is no upper limit to positive numbers; they go on infinitely.

Recognizing positive numbers on the number line helps in understanding how far they are from zero, which directly relates to their absolute value.

Calculating Distance from Zero

Distance from zero is a fundamental concept in understanding absolute value. It tells you how far a particular number is from zero, recorded as a non-negative value.
The distance is always a positive number because distance itself is not directional—it simply measures how much ground is covered. When you find the absolute value of a number, you concern yourself only with this distance, not the direction.

• For example, the distance from zero for 20 is 20 units.
• For -20, oddly enough, the distance is also 20 units. This highlights that the absolute value ignores the direction of the number relative to zero.

So, when asked for the absolute value of 20, you're asked for the distance 20 from zero, which is indeed 20 units.