5.10 1)
4x 460
3x+2>0
4x64
3x> 2
x 61
x >
2
3
S= ℄ 1;1℄
\ ℄ 2
3
;+1[
=℄ 2
3
;1℄
2)
x 2
10x+2160
x 2
6x+16>0
x 2
10x+2160
x 2
+6x 16<0
(x 3)(x 7)60
(x 2)(x+8)<0
x 2 +
x+8 +
P(x) + +
x 3 + +
x 7 +
P(x) + +
8
2
0 0
0 0
3 7
0
0
0 0
S= [3;7℄
\ ℄ 8;2[
=?
3) 8
>
>
<
>
>
:
3x 8
5 6x
>0
x 2
+1
x+1
>0
x 2
+1 + +
x+1 +
F(x) +
3x 8 +
5 6x +
F(x) +
1 5
6 8
3
0
0
S= ℄ 5
6
; 8
3
℄
\ ℄ 1;+1[
=℄ 5
6
; 8
3
℄
4) 8
<
:
4x 460
3x+12<0
x+8>3x+2
8
<
:
4x64
3x< 12
2x> 6
<
: x61
x< 4
x<3
S= ℄ 1;1℄
\ ℄ 1; 4[
\ ℄ 1; 3[
=℄ 1; 4[
5) 3<
7 x
x+3 63
8
>
<
>
: 3<
7 x
x+3
7 x
x+3 63
8
>
<
>
: 0<
7 x
x+3 +3
7 x
x+3
360
8
>
>
<
>
>
: 0<
(7 x)+3(x+3)
x+3
(7 x) 3(x+3)
x+3
60
8
>
<
>
: 0<
2x+16
x+3
4x 2
x+3 60
4x 2 + +
x+3 + +
F(x) +
2x+16 + +
x+3 +
F(x) + +
3 1
2
0
0
8 3
0
0
S= ℄ 1; 8[[℄ 3;+1[
\ ℄ 1; 3[[[ 1
2
;+1[
=℄ 1; 8[[[ 1
2
;+1[
6) (x 2)
2x+3
2 x
4x
61
(x 2)
(2x+3) 4x(2 x)
2 x
61
(x 2) 4x
2
6x+3
2 x
61
(x 2)(4x 2
6x+3)
2 x
160
(x 2)(4x 6x+3) 1(2 x)
2 x
60
(x 2)(4x 2
6x+3)+1(x 2)
2 x
60
(x 2)(4x 2
6x+4)
2 x
60
x 2 +
4x 2
6x+4 + + =( 6)
2
444= 28<0
2 x +
F(x)
2
S=R f2g=℄ 1;2[[℄2;+1[
7)
x 2
460
3x+2>0
(x 2)(x+2)60
x >
2
3
x 2 +
x+2 + +
P(x) + +
2
2
0 0
0 0
S=[ 2;2℄\℄ 2
3
;+1[=℄ 2
3
;2℄
8) 8
<
: 4x
2
4x6 1
x+7
2
>x 3
4x 2
4x+160
x+7>2x 6
(2x 1) 2
60
13>x
S=f 1
2
g\℄ 1;13[=f 1
2 g
9) 8
>
>
<
>
>
:
3x 5
2 6x
>0
x 2
+1
(x+1) 2
>1
>
>
<
>
>
:
3x 5
2 6x
>0
x 2
+1
(x+1) 2
1>0
8
>
>
<
>
>
:
3x 5
2 6x
>0
(x 2
+1) 1(x+1) 2
(x+1) 2
>0
8
>
>
<
>
>
:
3x 5
2 6x
>0
2x
(x+1) 2
>0
2x + +
(x+1) 2
+ + +
F(x) + +
3x 5 +
2 6x +
F(x) +
1
0
0
0 1
3 5
3
0
0
S=℄ 1
3
; 5
3
℄ \ ℄ 1; 1[[℄ 1;0[
=?
10) 3<1 x 2
63
3<1 x 2
1 x
2
63
0<4 x 2
06x 2
+2
0<(2 x)(2+x)
06x 2
+2
x 2
+2 + =0 2
412= 8<0
2 x + +
2+x + +
P(x) +
2
2
0 0
0 0
S=℄ 2;2[\R =℄ 2;2[
11) 8
<
:
9x 2<3x 14
5x+3<15 7x
11x 4>10x 9
8
<
:
6x< 12
12x<12
x> 5
<
:
x< 2
x<1
x> 5
S= ℄ 1; 2[
\ ℄ 1;1[
\ ℄ 5;+1[
=℄ 5; 2[
12) 8
>
>
<
>
>
:
4x 5
2 3x
>0
x 2
+4
x+2
>0
x 2
+4 + +
x+2 +
F(x) +
4x 5 +
2 3x +
F(x) +
2 2
3 5
4
0
0
S= ℄ 2
3
; 5
4
℄
\ ℄ 2;+1[
=℄ 2
3
; 5
4
℄
13) 8
>
>
>
>
>
<
>
>
>
>
>
:
(x+1) 3
3(x 1) 2
>x 3
11
3x 1
2
<x+
x 2
5
1+ 2
x 6
3
x 2
8
>
>
<
>
>
: x
3
+3x 2
+3x+1 3x 2
+6x 3>x 3
11
5(3x 1)<10x+2(x 2)
061+ 2
x +
3
x 2
8
>
>
<
>
>
: x
3
+9x 2>x 3
11
15x 5<10x+2x 4
06 x
2
+2x+3
x 2
8
>
>
<
>
>
:
9x> 9
3x<1
06 x
2
+2x+3
x 2
8
>
>
<
>
>
:
x> 1
x<
1
3
06 x
2
+2x+3
x 2
x 2
+2x+3 + + =2
2
413= 8<0
x 2
+ +
F(x) + +
S= ℄ 1;+1[
\ ℄ 1; 1
3 [
\ R f0g
=℄ 1;0[[℄0; 1
3 [
14) 8
>
>
<
>
>
:
(x+2)(6 x)>0
x 2
x 1260
x
x 2
9
>0
8
>
>
<
>
>
:
(x+2)(6 x)>0
(x 4)(x+3)60
x
(x 3)(x+3)
>0
x 4 +
x+3 + +
P(x) + +
x+2 + +
6 x + +
P(x) +
3
4
0 0
0 0
2
6
0
0
0 0
x + +
x 3 +
x+3 + + +
F(x) + +
3
0 3
0
0
S= [ 2;6℄
\ [ 3;4℄
\ ℄ 3;0[[℄3;+1[
=[ 2;0[[℄3;4℄
