Question

Cine ma poate ajuta sa rezolv inecuațiile de la punctul c, d, e?

Answer 1

Răspuns:

c. x≥0

d. x > $\frac{-3}{5}$

e. x∈[-4,-3/2) U[-1,∞)

Explicație pas cu pas:

c. $\frac{2}{x-1} + \frac{5x-3}{x-1}$≥1    / *(x-1)

2+5x-3≥x-1

5x-x≥-1+3-2

4x≥0

x≥0

d. $\frac{1}{2(x+2)} -\frac{2x+1}{x+2}$ < $\frac{1}{2}$   /*2(x+2)

1-2(2x+1) < x+2

1-4x-2 < x+2

-4x-x < 2+2-1

-5x < 3  /:(-5)

x > $\frac{-3}{5}$

e. $\frac{(x+4)(x+1)}{2x+3}$ > 0  

x      | -∞        -4         -3/2          -1        +∞

x+4  |------------0+++++++++++++++++++++

x+1   | ------------------------------------0++++++

2x+3|------------------------0++++++++++++++

ect.  |------------0+++++++/------------0+++++

x+4=0

x= -4

x+1=0

x= -1

2x+3=0

x= -3/2

x∈[-4,-3/2) U[-1,∞)