Question

Urgente!!!!!!!!!!!!! Preciso da resposta o mais rápido possível!!!!

Answer 1

1.
|3x - 2| < 4
3x - 2 < 4
3x < 6
x < 2

-3x + 2 < 4
-3x < 2
x > -2/3

S = {x E |R/ -2/3 < x < 2} ou]-2/3;2[

2.

|2x - 3| <= 1
2x - 3 <= 1
2x <= 4
x <= 2

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

S = {x E |R/ 1 >= x <= 2} ou [1;2]

3.

|x^2 - x - 4| > 2

x^2 - x - 4 > 2
x^2 - x - 6 > 0 (a = 1; b = -1 e c = -6)
delta = (b^2 - 4ac)
delta = (-1)^2 - 4•1•(-6)
delta = 1 + 24 = 25 => Vdelta = 5
x = (-b +/- Vdelta)/2a
x = (-(-1) +/- 5)/2•1
x = (1 +/- 5)/2
x’ = (1 - 5)/2 = -4/2 = -2
x’’ = (1 + 5)/2 = 6/2 = 3

S1 = {x E |R/ x < -2 e x > 3}

-x^2 + x + 4 > 2
-x^2 + x + 2 > 0 (a = -1; b = 1 e c = 2)
delta = b^2 - 4ac
delta = 1^2 - 4•(-1)•2 = 1 + 8 = 9 => Vdelta = 3
x = (-b +/- Vdelta/2a
x = (1 +/- 3)/2•(-1)
x = (1 +/- 3)/-2
x’ = (1 - 3)/-2 = -2/-2 = 1
x’’ = (1 + 3)/-2 = 4/-2 = -2

S2 = {x E |R/-2 < x < 1}

S1 = {x E |R/ x < -2 e x > 3} ]-2;3[
S2 = {x E |R/-2 < x < 1} ]-2;1[

S = {x E |R/ -2 < x < 1} ou ]-2;1[

4.

|2 - 3x|| >= 1
2 - 3x >= 1
-3x >= -1
3x <= 1
x <= 1/3

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

S = {x E |R/ x <= 1/3 e x >= 1} ou [-oo;1/3] e [1;+oo]

5.

|4x - 7| >= -1
4x - 7 >= -1
4x >= 6
x >= 3/2

-4x + 7 >= -1
-4x >= -8
4x <= 8
x <= 2

S = {x E |R/ 3/2 <= x <=2} ou [3/2;2]