Question

Решите неравенство:
1. |5-4x|≤8x+17 
2 $sqrt{3-x}$>5+3x

Answer 1

1
|5-4x|≤8x+17
1)x<1,25
5-4x≤8x+17
8x+4x≥5-17
12x≥-12
x≥-1
-1≤x<1,25
2)x≥1,25
4x-5≤8x+17
8x-4x≥-5-17
4x≥-22
x≥-5,5
x≥1,5
x∈[-1;∞)
2
√(3-x)>5+3x
{3-x≥0⇒x≤3
{3-x>25+30x+9x²⇒9x²+31x+22<0⇒-22/9<x<-1
D=961-792=169
x1=(-31-13)/18=-22/9 U x2=(-31+13)/18=-1
x∈(-22/9;-1)