知识点 4

Solve problems with absolute value, intervals, and inequality notation.

Translate absolute value inequalities into intervals and read the endpoint notation correctly.

核心知识

Absolute value measures distance from 0, so solve it by turning it into a two-sided inequality and then match the endpoint symbols to interval notation.

深入理解

Rule: An absolute value inequality is usually easiest if you translate it into a range.

For $| 𝑒 𝑥 𝑝 𝑟 𝑒 𝑠 𝑠 𝑖 𝑜 𝑛 | < 𝑎$ , the expression stays between $- 𝑎$ and $𝑎$ . For $| 𝑒 𝑥 𝑝 𝑟 𝑒 𝑠 𝑠 𝑖 𝑜 𝑛 | \leq 𝑎$ , the endpoints are included. After solving, read the symbols carefully when writing interval notation: parentheses mean the endpoint is not included, and brackets mean it is.

题目

示例解析

Which interval represents the solution to $| 2 𝑥 - 3 | \leq 7$ ?

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