解绝对值不等式,一般方法总是设法先去掉绝对值符号,变成普通不等式来解。但是,在特殊情况下,还可以用更简捷的方法来解。请看下面的定理(以下的关系符号“∨”,表示“>”,“<”,“≥”,“≤”…中的任一种)。定理.如果f(x)+φ(x)≥0,则不等式|f(x)|∨φ(x)与不等式f(x)∨φ(x)同解。 To solve the absolute value inequality, the general method always tries to remove the absolute value symbol first and become an ordinary inequality solution. However, in special circumstances, you can also use a more simple method to solve. Please see the following theorem (The following relationship symbol “∨” represents any one of “>”, “<”, “≥”, “≤”...). Theorem. If f(x) + φ(x) ≥ 0, the inequality |f(x)|∨φ(x) and the inequality f(x) ∨ φ(x) have the same solution.