Решите неравенство;|2х+1|<3; 2)|1-2х|<5; 3)|3х-2|>7; 4)|4+3х|>2; 5)|5х+3|<7; 6) |4х+3|>5

Question

Решите неравенство;|2х+1|<3; 2)|1-2х|<5; 3)|3х-2|>7; 4)|4+3х|>2; 5)|5х+3|<7; 6) |4х+3|>5

Answer 1

1)|2х+1|<3<br>-3<2x+1<3<br>-4<2x<2<br>-2x∈(-2;1)
2)|1-2х|<5<br>-5<1-2x<5<br>-6<-2x<4<br>-2x∈(-2;3)
3)|3х-2|>7
3x-2<-7 U 3x-2>7
3x<-5 U 3x>9
x<-5/3 U x>3
x∈(-∞;-5/3) U (3;∞)
4)|4+3х|>2
4+3x<-2 U 4+3x>2
3x<-6 U 3x>-2
x<-2 U x>-2/3
x∈(-∞;-2) U (-2/3;∞)
5)|5х+3|<7<br>-7<5x+3<7<br>-10<5x<4<br>-2x∈(-2;0,8)
6) |4х+3|>5
4x+3<-5 U 4x+3>5
4x<-8 U 4x>2
x<-2 U x>0,5
x∈(-∞;-20 U (0,5;∞)