Problem 1 Find $|-14|$ A. 14 \(B .-1... [FREE SOLUTION]

Chapter 2: Problem 1

Find $|-14|$ A. 14 $B .-14$ c. 0 D. $|4|$

Short Answer

Expert verified

The absolute value of |-14| is 14, which is option A.

Step by step solution

Understanding Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. Absolute values are always non-negative.

Apply the Absolute Value Definition

To find the absolute value of -14, remove the negative sign. The result is positive: |-14| = 14.

Compare with Given Options

Check the result, 14, against the options provided: A. 14, B. -14, C. 0, D. |4|. The correct answer is option A: 14.

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Key Concepts

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

Number Line

A number line is a visual tool used in mathematics to represent numbers in a straight line format. Each position on the line corresponds to a unique real number. The central point of a number line is zero, which serves as a reference point for identifying other numbers. Numbers to the right of zero are positive, and those to the left are negative.

Helps in visualizing mathematical operations
Makes understanding concepts like absolute value easier
Essential to grasping basic arithmetic and algebra concepts

Using a number line, we can easily visualize the concept of absolute value, which is essentially the distance of any number from zero.

Negative Numbers

Negative numbers are numbers less than zero, and are located to the left of zero on the number line. They are often used to represent quantities that have a deficit or decrease. In mathematics, negative numbers are as vital as positive numbers and are used in various applications such as

Temperature (e.g., -5掳C)
Financial calculations (e.g., a debt of -$100)
Elevation levels below sea level

When discussing absolute value, negative numbers are transformed into their positive counterparts by considering their magnitude, which is the true meaning of absolute value in mathematical terms.

Distance from Zero

The distance from zero is a phrase you might hear often when discussing absolute values. On a number line, the distance from zero measures how far a number is from the central point, zero. This measurement disregards direction (left or right), focusing solely on magnitude.

Every number has a specific distance from zero
This distance is expressed as an absolute value
Ensures values are always non-negative

Taking an example of $-14$, its distance from zero is 14 units, leading to the absolute value $|-14| = 14$. This proves that absolute values cannot be negative, as distance cannot be negative.

Non-negative Values

Non-negative values are numerical values that are either positive or zero. In mathematical terms, any non-negative value is zero or greater. Absolute value is inherently a non-negative function as it deals with the distance of numbers from zero, a concept that cannot yield negative results.

Includes all positive numbers and zero
Used to describe output of absolute value functions
Vital in ensuring measurements of distance remain positive

Understanding that the result of an absolute value function is always a non-negative value helps clarify why we disregard negative signs when calculating absolute values, such as $|-14| = 14$.

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91影视

Find \(|-14|\) A. 14 \(B .-14\) c. 0 D. \(|4|\)

Short Answer

Step by step solution

Understanding Absolute Value

Apply the Absolute Value Definition

Compare with Given Options

Key Concepts

Number Line

Negative Numbers

Distance from Zero

Non-negative Values

One App. One Place for Learning.

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