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代数式求值问题是初中数学考试中出现频率较高的题型。这种题的灵活性相当高,不仅涉及代数式的化简、变形和运算,还需要熟练地掌握各种技能。在教学中,教师通过代数式的变形和整合,使复杂的运算转化为简单的运算,有利于培养学生的思维能力和创新意识。一、借用整体思想求值例1:3x+2y=1+3m 12x+3y=1-m!2满足x+y<0,求m的取值范围。(2012年甘肃初一数学竞赛训练题)
The problem of algebraic expression evaluation is a higher frequency problem in the junior high school mathematics test. The flexibility of such questions is rather high. It involves not only algebraic simplifications, transformations, and calculations, but also skillful mastery of various skills. In teaching, teachers use algebraic transformation and integration to transform complex operations into simple operations, which is conducive to cultivating students’ thinking ability and innovation consciousness. First, use the overall idea to evaluate Example 1: 3x+2y=1+3m 12x+3y=1-m!2 satisfies x+y<0, find the value range of m. (2012 Gansu Junior Mathematical Competition Training Question)