Question

a nierownosci tego typu

2/x>1

3/x<-2

Answer 1

2/x > 1      x ≠ 0

2 /x - 1 > 0

2/x - x/x > 0

(2 - x)/x > 0

(2 - x) * x > 0

- x * (x - 2) > 0     /*(-1)

x(x - 2) < 0

 

+++             ++++  a = 1 > 0

-----o-------o------->

      0 ----- 2

 

x ∈ (0, 2)

 

3/x < - 2

3/x + 2 < 0

3/x + 2x/x < 0

(3 - 2x) / x < 0

(3  -2x) * x < 0

-x (2x - 3) < 0    /*(-1)

x(2x - 3) > 0

 

+++++                      +++++

--------o------------o--------->

          0 ----------- 3/2

 

x ∈ (-oo, 0) u (3/2, + oo)