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

1. Equations & Inequalities

Linear Inequalities

College Algebra

1. Equations & Inequalities

Linear Inequalities

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1:19 minutes

Problem 74

Textbook Question

Write each statement using an absolute value equation or inequality. q is no more than 8 units from 22.

Verified step by step guidance

Understand that the phrase 'no more than 8 units from 22' refers to the distance between q and 22 being less than or equal to 8.

Recall that the absolute value expression \(|q - 22|\) represents the distance between q and 22.

Set up the inequality to reflect the condition that this distance is no more than 8: \(|q - 22| \leq 8\).

This inequality states that the value of q is within 8 units of 22, either above or below.

The solution to this inequality will give the range of values for q that satisfy the condition.

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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 measures the distance of a number from zero on the number line, regardless of direction. It is denoted as |x|, where |x| = x if x is positive or zero, and |x| = -x if x is negative. This concept is crucial for understanding how to express distances in mathematical terms, particularly in equations and inequalities.

Inequalities

Inequalities express a relationship where one quantity is larger or smaller than another, using symbols like <, >, ≤, or ≥. In the context of the question, the phrase 'no more than' indicates a maximum distance, which translates into an inequality. Understanding how to manipulate and interpret inequalities is essential for solving problems involving ranges of values.

Distance from a Point

The concept of distance from a point in mathematics often involves determining how far a number is from a specified value. In this case, 'q is no more than 8 units from 22' implies that q can vary within a specific range around 22. This understanding is key to forming the correct absolute value equation or inequality that captures the specified distance.