Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:25 minutes

Problem 17

Textbook Question

Determine whether each statement is true or false. |25| = |-25|

Verified step by step guidance

Understand the concept of absolute value: The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

Calculate the absolute value of 25: \(|25| = 25\) because 25 is already a positive number.

Calculate the absolute value of -25: \(|-25| = 25\) because the absolute value makes the negative number positive.

Compare the two absolute values: Since both \(|25|\) and \(|-25|\) equal 25, they are equal.

Conclude that the statement \(|25| = |-25|\) is true because both sides of the equation are equal.

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Key Concepts

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

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|. For example, |5| equals 5, and |-5| also equals 5, indicating that both numbers are the same distance from zero.

Properties of Absolute Value

One key property of absolute values is that |a| = |b| if and only if a = b or a = -b. This means that two numbers can have the same absolute value if one is the negative of the other. This property is essential for comparing absolute values in equations or inequalities.

Equality of Absolute Values

When comparing the absolute values of two numbers, such as |25| and |-25|, we can determine their equality by evaluating each expression. Since both expressions yield the same result (25), we conclude that the statement is true, demonstrating that absolute values eliminate the effect of negative signs.