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SamCat237
@SamCat237
August 2022
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Помогите с неравенством, содержащим модуль)
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sedinalana
||3-x|-≤x-1
1)x>3
|x-3-2|≤x-1
|x-5|≤x-1
a)3<x<5
5-x≤x-1
2x≥6
x≥3
x∈(3;5)
2)x≥5
x-5≤x-1
0≤4
x∈[5;∞)
2)x≤3
|3-x-2|≤x-1
|1-x|≤x-1
a)x<1
-x+1≤x-1
2x≥2
x≥1
нет решения
b)1≤x≤3
x-1≤x-1
0≤0
x∈[1;3]
Ответ x∈[1;∞)
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Answers & Comments
1)x>3
|x-3-2|≤x-1
|x-5|≤x-1
a)3<x<5
5-x≤x-1
2x≥6
x≥3
x∈(3;5)
2)x≥5
x-5≤x-1
0≤4
x∈[5;∞)
2)x≤3
|3-x-2|≤x-1
|1-x|≤x-1
a)x<1
-x+1≤x-1
2x≥2
x≥1
нет решения
b)1≤x≤3
x-1≤x-1
0≤0
x∈[1;3]
Ответ x∈[1;∞)