Problem 45 Find the absolute value. $$ ... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 45

Find the absolute value. $$ |18| $$

Short Answer

Expert verified

|18| = 18

Step by step solution

Understand Absolute Value

The absolute value of a number is its distance from zero on the number line, without considering the direction. It is always a non-negative number.

Identify the Number

Here, the number given is 18.

Apply the Definition

Since the absolute value is the distance from zero, $ |18| $ means the distance of 18 from zero, which is 18 itself because 18 is already a positive number.

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Key Concepts

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

distance from zero

The concept of distance from zero is fundamental in understanding absolute value. Absolute value measures how far a number is from zero on the number line. This distance is always positive because distance cannot be negative. When we measure the absolute value, we count how many units a number is away from zero.
For instance, to find the absolute value of 18, we look at where 18 is on the number line and count the units back to zero. Since it's 18 units away, the absolute value $ |18| $ is 18.
Remember that the absolute value does not concern itself with direction, whether to the left or right of zero. It strictly measures distance.

non-negative number

An important aspect to grasp with absolute value is that it's always expressed as a non-negative number. This means that the result of an absolute value operation is never negative.
Let鈥檚 consider the number 18. Since 18 is already positive, the absolute value of 18 is simply 18. On the other hand, if we had a negative number like -18, finding the absolute value would mean ignoring the negative sign and recognizing the distance from zero, which is still 18. Thus, the absolute value of -18 is also 18.
The key takeaway is that the absolute value of any number, whether positive or negative, is always non-negative.

number line

The number line is a helpful tool to visualize the concept of absolute value. A number line is a straight line with zero at the center and numbers placed at uniform intervals both to the right (positive) and left (negative).
When you place 18 on this line, it sits 18 units to the right of zero. Whether you place -18, the absolute value still counts the number of units to zero, which sits 18 units to the left of zero.
By using a number line, you can see that the absolute value of a number represents the length of the segment between that number and zero, irrespective of direction.

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91影视

Find the absolute value. $$ |18| $$

Short Answer

Step by step solution

Understand Absolute Value

Identify the Number

Apply the Definition

Key Concepts

distance from zero

non-negative number

number line

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