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VergoLML
@VergoLML
July 2022
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Помогите решить неравенство с модулями.Знак ≤ 0
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sedinalana
Verified answer
(|x-10|+|5+x|-15)/(|x-11|+|9-x|-2)≤0
1)x<-5
(-x+10-5-x-15)/(-x+11+9-x-2)≤0
(-2x-10)/(-2x+18)≤0
(2x+10)/(2x-18)≤0
x=-5 x=9
+ _ +
---------------[-5]-------------(9)----------------
-5≤x<9 не удов усл
2)-5≤x<9
(-x+10+5+x-15)/(-x+11+9-x-2)≤0
0/(-2x+18)≤0
0≤0
x∈[-5;9)
3)9≤x<10
(-x+10+5+x-2)/(-x+11-9+x-2)≤0
0/0≤0
нет решения
4)10≤x≤11
(x-10+5+x-15)/(-x+11-9+x-2)≤0
(2x-20)/0≤0
нет решения
5)x>11
(x-10+5+x-15)/(x-11-9+x-2)≤0
(2x-20)/(2x-22)≤0
x=10 U x=11
+ _ +
-----------------[10]---------------(11)-----------
10≤x<11 не удов усл
Ответ x∈[-5;9)
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Answers & Comments
Verified answer
(|x-10|+|5+x|-15)/(|x-11|+|9-x|-2)≤01)x<-5
(-x+10-5-x-15)/(-x+11+9-x-2)≤0
(-2x-10)/(-2x+18)≤0
(2x+10)/(2x-18)≤0
x=-5 x=9
+ _ +
---------------[-5]-------------(9)----------------
-5≤x<9 не удов усл
2)-5≤x<9
(-x+10+5+x-15)/(-x+11+9-x-2)≤0
0/(-2x+18)≤0
0≤0
x∈[-5;9)
3)9≤x<10
(-x+10+5+x-2)/(-x+11-9+x-2)≤0
0/0≤0
нет решения
4)10≤x≤11
(x-10+5+x-15)/(-x+11-9+x-2)≤0
(2x-20)/0≤0
нет решения
5)x>11
(x-10+5+x-15)/(x-11-9+x-2)≤0
(2x-20)/(2x-22)≤0
x=10 U x=11
+ _ +
-----------------[10]---------------(11)-----------
10≤x<11 не удов усл
Ответ x∈[-5;9)