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Plum322
@Plum322
July 2022
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|х-1|-|х|<= -1 помогите с решением
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GreatFilter
X-1=0
x=1
x=0
x∈(-∞;0]
-(х -1)-(-х)≤
-1
-x+1+x
≤-1
1≤-1
нет решения
x∈(0;1]
-(х -1)-х≤ -1
-x+1-x≤-1
-2x≤-1-1
-2x≤-2
x≥1
x∈(0;1]
x=1
x∈(1;+∞)
+(х -1)-х≤ -1
x-1-x≤-1
-1≤-1
x∈R
x∈(1;+∞)
Ответ: х∈[1; +∞)
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Answers & Comments
x=1
x=0
x∈(-∞;0]
-(х -1)-(-х)≤ -1
-x+1+x≤-1
1≤-1
нет решения
x∈(0;1]
-(х -1)-х≤ -1
-x+1-x≤-1
-2x≤-1-1
-2x≤-2
x≥1
x∈(0;1]
x=1
x∈(1;+∞)
+(х -1)-х≤ -1
x-1-x≤-1
-1≤-1
x∈R
x∈(1;+∞)
Ответ: х∈[1; +∞)