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用距离的观点来解初等数学中的绝对不等式问题有准确、直观、快速的优点,作者在本刊1983年第4期《图象和代数不等式》一文中,曾有探讨。这里对此再作进一步讨论。称绝对值|x-a|为点x到数轴上点a的距离,称绝对值|x+a|为点x到数轴上点-a的距离。这样我们很容易解下面各种形式的问题,它将给初学者解这类问题带来方便并提供一个迅速有效的检验方法。例1.求不等式|x-5|<3的解。
The use of distance to solve the absolute inequality problem in elementary mathematics has the advantages of accuracy, intuition, and rapidity. The author has discussed it in the article “Image and Algebraic Inequality” in the 4th issue of this magazine in 1983. This is further discussed here. The absolute value |x-a| is the distance from the point x to the point a on the axis, and the absolute value |x+a| is the distance from the point x to the point -a on the axis. In this way, we can easily solve the following problems in various forms. It will provide convenience for beginners to solve such problems and provide a rapid and effective test method. Example 1. Find the solution of the inequality |x-5|<3.