若2x+|4-5x|+|1-3x|+4恒为常数,求x应满足的条件及常数的值

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若2x+|4-5x|+|1-3x|+4恒为常数,求x应满足的条件及常数的值若2x+|4-5x|+|1-3x|+4恒为常数,求x应满足的条件及常数的值若2x+|4-5x|+|1-3x|+4恒为常数,求x

若2x+|4-5x|+|1-3x|+4恒为常数,求x应满足的条件及常数的值
若2x+|4-5x|+|1-3x|+4恒为常数,求x应满足的条件及常数的值

若2x+|4-5x|+|1-3x|+4恒为常数,求x应满足的条件及常数的值
2x+|4-5x|+|1-3x|+4=k
注意到2x+(4-5x)+(3x-1)+4=2x+4-5x+3x-1+4=7=常数
所以只要令4-5x≥0且1-3x≤0即可
x≤4/5且x≥1/3
x的取值范围是1/3≤x≤4/5,常数的值是7

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