Question

1.|12x-11| = 1
2.|11-3x|= 2
3.|11x-5|<4
4.|5-7x|≤12
5.|7x-12|>5
6.|12+3x|≥3
7.||X-2|-1)=3
8.|(X(la patrat)+3x+2|= 0
Va rog frumos ajutați-mă!!

Answer 1

Explicație pas cu pas:

|12x-11|=1 =>

12x-11=1 sau 12x-11=-1 =>

12x=12 sau 12x=10 =>

x=1 sau x=5/6

|11-3x|=2 =>

11-3x=2 sau 11-3x=-2 =>

3x=9 sau 3x=13 =>

x=3 sau x=13/3

|11-5x|<4 => -4<11-5x<4 => -15<-5x<-7 =>

3>x>7/5 => x€(7/5;3)

|5-7x|<=12 => -12<=5-7x<=12 =>

-17<=-7x<=7 => 17/7>=x>=-1 =>

x€[-1;17/7]

|7x-12|>5 => 7x-12>5 sau 7x-12<-5 =>

7x>17 sau 7x<7 =>

x>17/7 sau x<1 =>

x€(17/7;+infinit)U(-infinit;1)

|12+3x|>=3 => 12+3x>=3 sau 12+3x<=-3 =>

3x>=-9 sau 3x<=-15 =>

x>=-3 sau x<=-5 =>

x€[-3,+infinit)U(-infinit;-5]

|x-2|-1=3 => |x-2|=4 => x-2=4 sau x-2=-4 =>

x=6 sau x=-2

|x²+3x+2|=0 => |x²+x+2x+2|=0 =>

|x(x+1)+2(x+1)|=0 =>

|(x+1)(x+2)|=0 => (x+1)(x+2)=0 =>

x+1=0 => x=-1

sau

x+2=0 => x=-2