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实数 a 的绝对值|a|,表示数轴上点 x 到原点的距离.|x-a|表示数轴上点 x 到点 a 的距离.在解题中.若注意实数绝对值的几何意义,可以避免冗长的讨论.下面仅举几例加以说明.例1(武汉、广州、福州三市联合竞赛题)已知|x-1|+|x-5|=4,求实数 x 的值.
The absolute value of the real number a |a| represents the distance from the point x on the axis to the origin. |xa| represents the distance from the point x to the point a on the axis. In the problem solving, the geometric meaning of the absolute value of the real number can be avoided. The following discussion is just a few examples to illustrate. Example 1 (joint contests in Wuhan, Guangzhou, and Fuzhou) Given |x-1|+|x-5|=4, find the value of the real number x.