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近年来各地中考试题中,围绕不等式(组)出现了一批既考查知识,又考查能力的新题型.现采撷一束,分类例举如下.一、新定义型例1(2013年十堰市)定义:对于实数a,符号[a]表示不大于a的最大整数.例如:[5.7]=5,[5]=5,[-π]=-4.(1)如果[a]=-2,那么a的取值范围是.(2)如果x+1[]2=3,求满足条件的所有正整数x.解(1)∵[a]=-2,∴a的取值范围是-2≤a<-1;(2)根据题意得3≤x+12<4,解得5≤x<7,则满足条件的所有正整数为5、6.说明本题设置了新定义,考查一元一次不等式组的应用,解题的关键是根据题意列出不等式组,求出不等式的解.
In recent years around the examination questions, around the inequality (group) appeared a number of both knowledge and ability to examine a new type of test now pick a bunch, the classification is as follows: First, the new definition Example 1 (Shiyan City in 2013 ) Definition: For the real number a, the symbol [a] represents the largest integer not larger than a. For example: [5.7] = 5, [5] = 5, [- π] = - 4. (1) 2, then the range of a is 2. (2) If x + 1 [] 2 = 3, find all positive integers satisfying the condition x. Solution (1) ∵ [a] = - 2, the range of ∴a Is -2 ≤ a <-1; (2) According to the title of 3 ≤ x + 12 <4, to solve 5 ≤ x <7, then all the positive integers satisfying the condition are 5, 6. , Examining the application of a unitary inequality group, the key to solving the problem is to list the inequality group according to the title, to solve the inequality.