Textbook Question
Write each number in decimal notation without the use of exponents.
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 69
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. −2 and 5
Verified step by step guidance1
Identify the two numbers given: -2 and 5.
Recall that the distance between two numbers \(a\) and \(b\) on the number line can be expressed as the absolute value of their difference: \(\left| a - b \right|\) or \(\left| b - a \right|\).
Write the distance between -2 and 5 as an absolute value expression: \(\left| -2 - 5 \right|\) or \(\left| 5 - (-2) \right|\).
Simplify inside the absolute value: \(\left| -2 - 5 \right| = \left| -7 \right|\) or \(\left| 5 + 2 \right| = \left| 7 \right|\).
Evaluate the absolute value: \(\left| -7 \right| = 7\) or \(\left| 7 \right| = 7\), which gives the distance between the two numbers.
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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. For numbers a and b, the distance is |a - b|, which ensures the result is non-negative and reflects the actual gap between the points.
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Evaluating Absolute Value Expressions
To find the distance, first write the absolute value expression representing the difference between the numbers. Then calculate the difference inside the bars and take its absolute value, converting any negative result to positive to get the final distance.
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Related Practice
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In Exercises 67–82, find each product. (3x−y)(2x+5y)
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Evaluate each expression 27^(-4/3)
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Textbook Question
Simplify using properties of exponents.
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In Exercises 65–92, factor completely, or state that the polynomial is prime. 2x4−162
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In Exercises 69–82, simplify each complex rational expression. (x/3−1)/(x−3)