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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 4
Chapter 2, Problem 4

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | > 7
Matching exercise showing absolute value equations and inequalities paired with number line graphs of their solution sets.

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1
Understand the inequality \(|x| > 7\). This means the distance of \(x\) from 0 on the number line is greater than 7.
Rewrite the inequality without the absolute value: \(x > 7\) or \(x < -7\).
Interpret the solution set as two separate intervals: one interval where \(x\) is greater than 7, and another where \(x\) is less than -7.
On a number line graph, represent these intervals by shading the regions to the right of 7 and to the left of -7, excluding the points 7 and -7 themselves (since the inequality is strict).
Match this description to the graph in Column II that shows two rays extending outward from -7 and 7, with open circles at these points.

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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 with absolute value symbols, such as |x| > 7. It represents the distance of x from zero on the number line. For |x| > 7, the solution includes all x values whose distance from zero is greater than 7.
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Graphing Solution Sets on a Number Line

Graphing solution sets for inequalities involves shading regions on a number line that satisfy the inequality. For |x| > 7, the graph shows two rays extending left from -7 and right from 7, excluding the interval between -7 and 7.
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Inequality Notation and Interpretation

Understanding inequality notation like >, <, ≥, and ≤ is essential to interpret solution sets correctly. The inequality |x| > 7 means x is either less than -7 or greater than 7, which translates to two separate intervals on the number line.
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