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含绝对值的代数式是中考数学及竞赛中的常见题目,在这些题目当中,大多情况下是去掉绝对值符号进行解题,如何去掉绝对值符号呢?下面归纳举例。一、定义型: 若|φ(x)|=φ(x),则φ(x)≥0;若|φ(x)|=-φ(x),则φ(x)≤0。例1 方程|x-3|+x-3=O的实数解有( ) (A)1个.(B)2个.(C)3个.(D)无数个. 略解:原方程变为|x-3|=-(x-3) 故x-3≤0,∴x≤3.故选D.
Algebraic expressions with absolute values are common topics in mathematics and competitions in Chinese exams. Among these topics, most of the time, the problem is solved by removing the absolute value signs. How do you remove the absolute value signs? The examples are summarized below. First, the definition type: If |φ(x)|=φ(x), then φ(x)≥0; if |φ(x)|=-φ(x), then φ(x)≤0. Example 1 The real solution of the equation |x-3|+x-3=O is () (A) 1 (B) 2 (C) 3 (D) Innumerable. Slight solution: The original equation becomes |x-3|=-(x-3) So x - 3 ≤ 0, ∴ x ≤ 3. Select D.