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Ch. 1 - Equations and Inequalities
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 1 - Equations and InequalitiesProblem 5
Chapter 2, Problem 5

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | < 7
List of absolute value equations and inequalities matched with number line graphs showing solution sets between -7 and 7.

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1
Understand the inequality given: \(|x| < 7\) means the distance of \(x\) from 0 on the number line is less than 7.
Rewrite the absolute value inequality without the absolute value bars: \(|x| < 7\) is equivalent to \(-7 < x < 7\).
Interpret this as a compound inequality representing all \(x\) values strictly between \(-7\) and \(7\).
Look for the graph in Column II that shows all points between \(-7\) and \(7\) (not including \(-7\) and \(7\) themselves), typically represented by an open interval on the number line.
Match the inequality \(|x| < 7\) with the graph that displays the solution set as the open interval \((-7, 7)\).

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Key Concepts

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

Absolute Value Inequalities

An absolute value inequality involves expressions like |x| < a, which means the distance of x from zero is less than a. This translates to a compound inequality -a < x < a, representing all values between -a and a on the number line.
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Graphing Solution Sets on the Number Line

Graphing solution sets involves shading the region of the number line that satisfies the inequality. For |x| < 7, the graph shows all points between -7 and 7, typically represented with an open or closed interval depending on the inequality.
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Compound Inequalities

Compound inequalities combine two inequalities joined by 'and' or 'or'. The inequality |x| < 7 is equivalent to -7 < x < 7, a conjunction that restricts x to values between -7 and 7, which helps in identifying the correct graph.
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