Table of contents

0. Review of Algebra4h 16m
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 19m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Graphs and Coordinates

College Algebra

2. Graphs of Equations

Graphs and Coordinates

1:10 minutes

Problem 67

Textbook Question

Write an equation involving absolute value that says the distance between p and q is 2 units.

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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 is a mathematical function that measures the distance of a number from zero on the number line, regardless of direction. It is denoted by two vertical bars, e.g., |x|. For any real number x, |x| = x if x is positive or zero, and |x| = -x if x is negative. This concept is crucial for understanding how distances are represented in equations.

Distance Formula

The distance formula calculates the distance between two points on a number line or in a coordinate system. In one dimension, the distance between two points p and q can be expressed as |p - q|. This formula is foundational for formulating equations that describe the relationship between points based on their distances.

Setting Up Equations

Setting up equations involves translating a verbal or conceptual statement into a mathematical expression. In this case, stating that the distance between p and q is 2 units translates to the equation |p - q| = 2. Understanding how to create and manipulate equations is essential for solving problems in algebra.