Question

resolva a inequação de 1 grau em N
(2x+1)/3x-1>-1

Answer 1

resolva a inequação de 1 grau em N 
(2x+1)/3x-1>-1

2x + 1
--------  > - 1
3x - 1                       mmc = 3x - 1

A = 2x + 1 > -1(3x -1)      
----------------------
B =         3x - 1

A
2x + 1 > - 3x + 1
2x + 3x + 1 >  + 1
2x + 3x > +1 - 1
2x + 3x > 0
5x > 0
A = x > 0

B = 3x - 1 > 0
3x > 1
B = x > 1/3

                           0                   1/3
             ------------|-----------------|---------------- 
      A = ------------o/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
      B =------------------------------o/\/\/\/\/\/\/\/\/\/\/\/
A∩B  = ------------------------------o/\/\/\/\/\/\/\/\/\/\/\

V = { x ∈R | 1/3 < x}   =    ] 1/3, ∞₊[              

Answer 2

$\frac{2x+1}{3x-1}>-1\\\\\frac{2x+1}{3x-1/1}+\frac{1}{1/(3x-1)}>0\\\\\frac{2x+1+3x-1}{3x-1}>0\\\\\frac{5x}{3x-1}>0$

Numerador:

$5x>0\\x>0$


Denominador:

$3x-1>0\\3x>1\\x>\frac{1}{3}$
 
 
 Por fim, 

__-______(0)__+__________+____
___-_________-_____(1/3)__+_____
___+____(0)__-_____(1/3)___+________

S = {x E R | x < 0 v x > 1/3, x # 1/3}