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 \(|x| \leq 7\). The absolute value \(|x|\) represents the distance of \(x\) from 0 on the number line, so this inequality means the distance from 0 is less than or equal to 7.

Rewrite the inequality without the absolute value by considering the definition: \(|x| \leq 7\) is equivalent to \(-7 \leq x \leq 7\).

Interpret the solution set \(-7 \leq x \leq 7\) as all real numbers \(x\) between -7 and 7, including the endpoints -7 and 7.

Look for the graph in Column II that shows a line segment or interval on the number line starting at -7 and ending at 7, with solid dots or closed circles at both ends to indicate inclusion of the endpoints.

Confirm that the graph matches the interval \([-7, 7]\) and that no other graphs represent this solution set.

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주요 개념

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

Absolute Value Inequality

An absolute value inequality like |x| ≤ 7 represents all values of x whose distance from zero on the number line is less than or equal to 7. This means x lies between -7 and 7, inclusive. Understanding this helps in identifying the solution set as an interval.

Interval Notation and Graphing

Interval notation expresses the set of solutions compactly, such as [-7, 7] for |x| ≤ 7. Graphing this interval on a number line involves shading all points between -7 and 7, including the endpoints, to visually represent the solution set.

Matching Equations to Graphs

Matching equations or inequalities to their graphs requires recognizing the solution set's shape and boundaries. For |x| ≤ 7, the graph is a line segment from -7 to 7. This skill involves interpreting algebraic expressions and linking them to their visual representations.