Помогите решить неравенство. 3/|х-1|>=2х+5. Created by PolinaTorkhunova. algebra-ru

|х-1|>=2х+5...

PolinaTorkhunova @PolinaTorkhunova

August 2022 1 20 Report

Помогите решить неравенство.
3/|х-1|>=2х+5

Answers & Comments

sedinalana

Verified answer

3/|x-1|≥2x+5
1)x<1
3/(1-x)≥2x+5
3/(1-x) -(2x+5)≥0
(3-2x-5+2x²+5x)/(1-x)≥0
(2x²+3x-2)/(x-1)≤0
2x²+3x-2=0
D=9+16=25
x1=(-3-5)/4=-2 U x2=(-3+5)/4=0,5
x-1=0⇒x=1
   _ + _ +
----------------[-2]-----------[0,5]-----------(1)-------------------
/////////////////////////////////////////////////////////////
x∈(-∞;-2] U [0,5;1)
2)x>1
3/(x-1)-(2x+5)≥0
(3-2x²-5x+2x+5)/(x-1)≥0
(2x²+3x-8)/(x-1)≤0
2x²+3x-8=0
D=9+64=73
x1=(-3-√73)/4 U x2=(-3+√73)/4
x-1=0⇒x=1
   _ + _    +
-------------[(-3-√73)/4]-------------(1)-------------[(-3+√73)/4]-----------------
   /////////////////////////////////////////////////////
x∈(1;(-3+√73)/4]
Ответ x∈(-∞;-2] U [0,5;1) U (1;(-3+√73)/4]

1 votes Thanks 1

PolinaTorkhunova Почему в первом случае |x-1| заменяется на 1-х?

sedinalana потому что под модулем отрицательное значение

PolinaTorkhunova А здесь почему знак поменялся?

PolinaTorkhunova (3-2x-5+2x²+5x)/(1-x)≥0
(2x²+3x-2)/(x-1)≤0

Answers & Comments

Verified answer

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