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hoganjohnson007
@hoganjohnson007
August 2022
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ПОЖАЛУЙСТА!!!ПОМОГИТЕ С МОДУЛЬНЫМИ НЕРАВЕНСТВАМИ!!!!
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sedinalana
Verified answer
|x+2|-|x-3|≥2x-1
1)x≤-2
-x-2+x-3≥2x-1
2x≤-5+1
2x≤-4
x≤-2
2)-2<x≤3
x+2+x-3≥2x-1
2x-2x≥-1+1
0≥0
3)x>3
x+2-x+3≥2x-1
2x≤-1+1
2x≤0
x≤0 не удов усл
x∈(-∞;3]
|x-3|+2>0
|x-3|>-2
x∈(-∞;∞)
|x-1|+|x-3|<x+1
x<1
-x+1-x+3<x+1
x+2x>4-1
3x>3
x>1 не удов усл
2)1≤x≤3
x-1-x+3<x+1
x>2-1
x>1
3)x>3
x-1+x-3<x+1
2x-x<1+4
x<5
x∈(1;5)
0 votes
Thanks 0
LFP
в первом неравенстве случай 3)x>3 ошибка!!! на ответ, правда, не повлияла, но все же...
LFP
2х ≤ 6 (должно быть...) х ≤ 3 --не уд.условию)))
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Answers & Comments
Verified answer
|x+2|-|x-3|≥2x-11)x≤-2
-x-2+x-3≥2x-1
2x≤-5+1
2x≤-4
x≤-2
2)-2<x≤3
x+2+x-3≥2x-1
2x-2x≥-1+1
0≥0
3)x>3
x+2-x+3≥2x-1
2x≤-1+1
2x≤0
x≤0 не удов усл
x∈(-∞;3]
|x-3|+2>0
|x-3|>-2
x∈(-∞;∞)
|x-1|+|x-3|<x+1
x<1
-x+1-x+3<x+1
x+2x>4-1
3x>3
x>1 не удов усл
2)1≤x≤3
x-1-x+3<x+1
x>2-1
x>1
3)x>3
x-1+x-3<x+1
2x-x<1+4
x<5
x∈(1;5)