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SAHARIA
@SAHARIA
November 2021
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Решить неравенство с модулем:
|x|-2|x-1|+4|x-3|<5x
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sangers1959
Verified answer
|x|-2*|x-1|+4*|x-3|<5x
Подмодульные выражения равны нулю при:
x=0 x=1=0 x=1 x-3=0 x=3
-∞__________0__________1___________3___________+∞
x∈(-∞;0)
-x-2*(-x+1)+4*(-x+3)<5x
-x+2x-2-4x+12<5x
8x>10
x>1,25∉
x∈(0;1])
x-2(-x+1)+4*(-x+3)<5x
x+2x-2-4x+12<5x
7x>10
x>1³/₇∉
x∈(1;3)
x-2*(x-1)+4*(-x+3)<5x
x-2x+2-4x+12<5x
10x>14
x>1,4 ⇒ x∈(1,4;3)
x∈[3;+∞)
x-2*(x-1)+4*(x-12)<5x
x-2x+2+4x-12<5x
2x>-10
x>-5 ⇒ x∈[3;+∞)
Ответ: x∈(1,4;+∞).
1 votes
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Answers & Comments
Verified answer
|x|-2*|x-1|+4*|x-3|<5xПодмодульные выражения равны нулю при:
x=0 x=1=0 x=1 x-3=0 x=3
-∞__________0__________1___________3___________+∞
x∈(-∞;0)
-x-2*(-x+1)+4*(-x+3)<5x
-x+2x-2-4x+12<5x
8x>10
x>1,25∉
x∈(0;1])
x-2(-x+1)+4*(-x+3)<5x
x+2x-2-4x+12<5x
7x>10
x>1³/₇∉
x∈(1;3)
x-2*(x-1)+4*(-x+3)<5x
x-2x+2-4x+12<5x
10x>14
x>1,4 ⇒ x∈(1,4;3)
x∈[3;+∞)
x-2*(x-1)+4*(x-12)<5x
x-2x+2+4x-12<5x
2x>-10
x>-5 ⇒ x∈[3;+∞)
Ответ: x∈(1,4;+∞).