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在高一第一章数学学习中,有一类含参数的绝对值不等式的解法颇令学生费解,现对其解法从思维障碍的角度做简单探讨。一、问题:若不等式|x+1|-|x-2|>k恒成立求k的取值范围。分析:含有两个绝对值号并且有参数的不等式在求解时,由于“绝对值号”和“参数”的多重困扰,所以求解比较困难,有以下几种解法。解法一:分类讨论令x+1=0得x=-1;令x-2=0得x=2
In the first chapter of higher mathematics learning, there is a class of parameters with absolute inequality of the solution is quite difficult for students to understand, and now its solution from the perspective of thinking disorders to do a simple discussion. First, the question: If the inequality | x + 1 | - | x-2 |> k constant k value of the establishment of the range. Analysis: Inequality with two absolute value numbers and parameters When solving, it is difficult to solve because of the multiple problems of “absolute value ” and “parameter ”. There are several solutions. Solution 1: Category Discussion Let x + 1 = 0 be x = -1; Let x-2 = 0 be x = 2