Problem 54 - Beginning and Intermediate Algebra

Question

Find each absolute value. |-14|

Step-by-Step Solution

Answer

The absolute value of -14 is 14.

Step 1: Understand Absolute Value

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

Step 2: Identify the Number

The given number is -14. We need to find the absolute value of this number.

Step 3: Apply the Definition of Absolute Value

Since absolute value measures distance and is always non-negative, we remove the negative sign from -14.

Step 4: State the Absolute Value

Therefore, the absolute value of -14 is 14.

Key Concepts

distance from zero

Absolute value is a concept in mathematics that refers to how far a number is from zero, without considering direction. Imagine standing on a number line. Zero is your starting point.
No matter if you walk to the right (positive) or to the left (negative), you're counting the steps you take. That count is your distance from zero.

For example, if we take the number -14 and think about its absolute value, we're looking at how far -14 is from zero.
Since we only count distance and disregard direction, we're looking at 14 steps. Hence, the absolute value of -14 is 14. Every absolute value is non-negative.
No matter how negative the original number is, the distance from zero cannot be negative because distance is always a positive value or zero.

number line

A number line is a visual representation of numbers laid out in a straight line. It helps us easily see and understand concepts like absolute value.
Imagine a long horizontal line with zero at the center. Positive numbers are placed to the right of zero, and negative numbers to the left.

When we talk about absolute values on a number line, we're measuring the distance to zero. For example, -14 is located 14 units to the left of zero.
Despite being on the left, the only thing that matters for absolute value is the distance, which is 14 units.
The same applies to positive numbers. For example, |14| is 14 because it's 14 units to the right of zero.

non-negative numbers

Non-negative numbers are numbers that are not negative. This includes all positive numbers as well as zero.
In the context of absolute value, it's important to know that the result is always non-negative.

When you take the absolute value of any number, whether it’s positive or negative, the result is always zero or a positive number.
For instance:

• |-14| = 14
• |0| = 0
• |14| = 14

Notice that regardless of the starting point, the absolute value results are all non-negative.
This is because we are measuring distance, and distance cannot be negative.