Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | > 7

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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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.