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绝对值化简是初中数学中的难点之一,本文将此类问题大致归纳为以下十种情况,进行举例分析.一、已知不等式的解集,化简绝对值例1已知:x<-1,化简:|3x+1|-|1-3x|.分析要去掉题中绝对值,明确3x+1,1-3x的符号是关键.这里根据条件,运用不等式的性质就可以得出求出3x+1,1-3x的符号.根据不等式的性质2,由x<-1,得3x<-3.又根据不等式的性质1,得3x+1<-2,这就确定了3x+1的符号为负号.
The reduction of absolute value is one of the difficulties in junior high school mathematics.This paper generalizes such problems into the following ten cases and gives an example analysis.One known solution of inequality, -1, Simplify: | 3x + 1 | - | 1-3x |. Analysis To remove the absolute value of the question, it is crucial to clarify the sign of 3x + 1,1-3x. Here, depending on the conditions, the nature of the use of inequalities Find 3x + 1,1-3x symbols. According to the nature of the inequality 2, from x <-1, 3x <-3. According to the nature of the inequality 1, 3x + 1 <-2, which determines the The sign of 3x + 1 is the minus sign.