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在解形如|ｆ(ｘ)|ｇ(ｘ)及|ｆ(ｘ)|ｇ(ｘ)的不等式时,往往会采取下列等价变换:|ｆ(ｘ)|ｇ(ｘ)ｇ(ｘ)0,-ｇ(ｘ)ｆ(ｘ)ｇ(ｘ).|ｆ(ｘ)|ｇ(ｘ)ｇ(ｘ)≥0,ｆ(ｘ)ｇ(ｘ)或ｆ(ｘ)-ｇ(ｘ);或ｇ(ｘ)0.这样做依据的是如下性质:不等式|ｘ|ａ(ａ0)的解集是{ｘ|-ａｘａ}.不等
When we solve the inequality of |f(x)|g(x) and |f(x)|g(x), the following equivalent transformations are often taken: |f(x)|g(x)g(x) ) 0, -g(x)f(x)g(x).|f(x)|g(x)g(x)≥0, f(x)g(x) or f(x)-g( x); or g(x)0. This is based on the following property: the inequality |x|a(a0) has a solution set of {x|-axa}.