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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1:08 minutes

Problem 12

Textbook Question

Evaluate each expression. |-15|

Verified step by step guidance

Understand that the vertical bars around -15 represent the absolute value, which is the distance of a number from zero on the number line.

Recall that the absolute value of a number is always non-negative.

Since -15 is 15 units away from zero on the number line, its absolute value is 15.

Therefore, the expression |-15| evaluates to 15.

Conclude that the absolute value operation removes any negative sign from the number.

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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 two vertical bars surrounding the number, such as |x|. For example, |5| equals 5, and |-5| also equals 5, indicating that both numbers are 5 units away from zero.

Properties of Absolute Value

Absolute value has specific properties that are useful in mathematical operations. One key property is that |a| = a if a is non-negative, and |a| = -a if a is negative. This means that the absolute value function transforms negative inputs into positive outputs, which is essential for evaluating expressions involving negative numbers.

Evaluating Expressions

Evaluating an expression involves substituting values into the expression and simplifying it to find a numerical result. In the case of |-15|, you apply the definition of absolute value to determine the output. This process is fundamental in algebra, as it allows for the analysis and solution of various mathematical problems.