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Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. P - Fundamental Concepts of AlgebraProblem 12
Chapter 1, Problem 12

Express the distance between the numbers -17 and 4 using absolute value. Then evaluate the absolute value.

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1
Recall that the distance between two numbers on the number line can be expressed as the absolute value of their difference. So, the distance between -17 and 4 is \(\left| -17 - 4 \right|\) or equivalently \(\left| 4 - (-17) \right|\).
Write the expression for the distance using absolute value: \(\left| -17 - 4 \right|\).
Simplify inside the absolute value: calculate \(-17 - 4\) which is \(-21\), so the expression becomes \(\left| -21 \right|\).
Recall the definition of absolute value: \(\left| x \right|\) is the distance of \(x\) from zero on the number line, which is always non-negative.
Evaluate the absolute value: \(\left| -21 \right|\) equals 21, which is the distance between -17 and 4.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is always non-negative and is denoted by vertical bars, for example, |x|. This concept helps measure how far apart two numbers are without considering which is larger.
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Distance Between Two Numbers

The distance between two numbers on the number line is the absolute value of their difference. It is calculated as |a - b|, ensuring the result is non-negative and reflects the actual gap between the points, regardless of their order.
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Evaluating Absolute Value Expressions

To evaluate an absolute value expression, first compute the value inside the bars, then take its non-negative magnitude. For example, | -21 | equals 21 because the distance from zero is 21, even though the number is negative.
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