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

1. Equations & Inequalities

Linear Inequalities

College Algebra

1. Equations & Inequalities

Linear Inequalities

1:17 minutes

Problem 124

Textbook Question

Write each statement using an absolute value equation or inequality. p is at least 3 units from 1.

Verified Solution

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

Absolute Value

Absolute value measures the distance of a number from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|, which equals x if x is positive or zero, and -x if x is negative. Understanding absolute value is crucial for solving equations and inequalities that involve distance.

Inequalities

Inequalities express a relationship where one quantity is larger or smaller than another, using symbols like >, <, ≥, or ≤. In the context of absolute value, inequalities can describe conditions where a variable must be a certain distance from a point, which is essential for interpreting statements about distance.

Distance from a Point

The concept of distance from a point on the number line is fundamental in absolute value equations and inequalities. When a statement specifies that a variable is 'at least' a certain distance from a point, it translates into an absolute value expression that captures both directions from that point, allowing for a complete representation of the condition.