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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0:57 minutes

Problem 69

Textbook Question

Write each statement using an absolute value equation or inequality. . m is no more than 2 units from 7.

Verified step by step guidance

Start by understanding the phrase 'no more than 2 units from 7'. This means the distance between m and 7 is at most 2.

The absolute value expression for the distance between m and 7 is |m - 7|.

Since m is no more than 2 units away from 7, we can write the inequality as |m - 7| \leq 2.

This inequality represents all values of m that are within 2 units of 7 on the number line.

The solution to this inequality will be the set of all m values 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 Definition

Absolute value measures the distance of a number from zero on the number line, regardless of direction. For any real number x, the absolute value is denoted as |x| and is defined as |x| = x if x ≥ 0, and |x| = -x if x < 0. This concept is crucial for translating statements about distance into mathematical equations or inequalities.

Distance in Mathematics

In mathematics, distance can be expressed as the absolute difference between two numbers. When stating that a number m is 'no more than' a certain distance from another number, it implies a range of values that m can take. This understanding is essential for forming the correct absolute value equation or inequality based on the given conditions.

Inequalities and Equations

Inequalities express a relationship where one quantity is less than, greater than, or equal to another. In this context, the phrase 'no more than' indicates a maximum limit, which can be represented using an inequality. Understanding how to formulate both equations and inequalities is key to accurately representing the given statement about m's distance from 7.