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对形如|x-a|+|x-b|=c(其中a0)的方程,一般采用讨论式求解．例如|x-2|+|x-5|=4．解(1)分区间:以x=2、5为端点,将数轴分为3个区间:x<2;2≤x<5;x≥5．(2)分类讨论:①当x<2时,原方程为2-x+5-x=4,解得x=1．5,由于1．5属于区间x<2,即在x<2范围内方程有解x=1．5;②当2≤x<5时,原方程为x-2+5- x=4,得3=4,这是个矛盾等式,即在2≤x<5范围内方程无解;③当x≥5时,原方程为x-2+x-5=4,得x=5．5,由于5．5属于区间x≥5,即在x≥5范围内方程的解为x=5．5．
For equations of the form |x-a|+|x-b|=c (where a0), they are generally solved by discussion. For example, |x-2|+|x-5|=4. Solution (1) Between partitions: Take x=2 and 5 as the endpoints, divide the number axis into 3 intervals: x<2; 2≤x<5; x≥5. (2) Classification Discussion: 1 When x<2, the original equation is 2-x+5-x=4, and the solution is x=1.5. Since 1.5 belongs to the interval x<2, ie, it is in the range of x<2. The inner equation has the solution x=1.5; 2 When 2≤x<5, the original equation is x-2+5-x=4, which yields 3=4. This is a contradictory equation, that is, 2≤x<5. There is no solution in the range equation; 3 When x ≥ 5, the original equation is x-2+x-5=4, get x=5.5, since 5.5 belongs to the interval x ≥ 5, that is, in the range of x ≥ 5 The solution of the equation is x=5.5.