помогите 1104 и 1105 срочно. Created by ILOVEVAPE. matematika-ru

помогите 1104 и 1105 срочно...

ILOVEVAPE @ILOVEVAPE

July 2022 1 1 Report

помогите 1104 и 1105 срочно

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TARTILLO

Verified answer

1104.
1) -3<1+2x<4 ⇔ -4<2x<3 -2<x<3/2
2) 1≤3-x≤5 ⇔ -5≤x-3≤-1 -2≤x≤2
3)-7<2x-5≤1 ⇔ -2<2x≤6    -1<x≤3

1105

1) 3≤ I x+4 I≤5

   I x+4 I²≤5² x²+8x+16-25≤0
{   ⇔   ⇔
I x+4 I²≥3² x²+8x+16-9≥0

+ - +
(x-1)(x+9)≤0 --------[-9]////////////////////////////////////////////////[1]------
{ ⇔ + - +
(x+7)(x+1)≥0 /////////////////////[-7]-----------------[-1]//////////////////////////

x∈[-9;-7]∪[-1;1]

2) 5<Ix-3I<8 ⇔ 5²<(x-3)² x²-6x+9-25>0 (x-8)(x+1)>0
{ { {
(x-3)²<8² x²-6x+9-64<0 (x-11)(x+5)<0
+ - +
(x-8)(x+1)>0 /////////////////////////(-1)---------------------(8)////////////////////////
+ - +
(x-11)(x+5)<0  -------------(-5)////////////////////////////////////////////////////////(11)------
x∈(-5;-1)∪(8;11)

3) 2<Ix-1I≤5 ⇔ (x-1)²≤5² x²-2x+1-25≤0
{   ⇔ {
(x-1)²>2² x²-2x+1-4>0
+ _ +
x²-2x-24≤0 (x-6)(x+4)≤0 --------------[-4]//////////////////////////////////[6]--------------
+ - +
x²-2x-3>0 ( x-3)(x+1)>0   //////////////////////////(-1)------------(3)/////////////////////////

x∈[-4;-1)∪(3;6]

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