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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1:23 minutes

Problem 57

Textbook Question

In Exercises 51–60, rewrite each expression without absolute value bars. -3/|-3|

Verified step by step guidance

Step 1: Recall the definition of absolute value. The absolute value of a number is its distance from 0 on the number line, regardless of direction. For any number x, |x| = x if x ≥ 0, and |x| = -x if x < 0.

Step 2: Identify the value inside the absolute value bars. In this case, the expression inside the absolute value bars is -3.

Step 3: Determine whether the value inside the absolute value bars is positive or negative. Since -3 is less than 0, the absolute value of -3 is |-3| = -(-3) = 3.

Step 4: Replace the absolute value expression with its evaluated result. The expression -3/|-3| becomes -3/3.

Step 5: Simplify the fraction -3/3 by dividing the numerator and denominator by their greatest common divisor, which is 3. This simplifies the expression further.

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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|, and is always non-negative. For example, |3| = 3 and |-3| = 3, illustrating that both positive and negative values yield the same absolute value.

Properties of Absolute Value

Absolute value has specific properties that are useful in simplifying expressions. One key property is that for any real number x, the absolute value can be expressed as |x| = x if x is non-negative, and |x| = -x if x is negative. This understanding is crucial for rewriting expressions that involve absolute values.

Simplifying Expressions

Simplifying expressions involves rewriting them in a more manageable form without changing their value. In the context of absolute values, this means applying the properties of absolute value to eliminate the bars. For instance, in the expression -3/|-3|, recognizing that |-3| equals 3 allows for straightforward simplification.