Bonjour
résoudre dans R les inéquations suivantes.
1
------->0
4x+1
4x + 1 # 0
4x # -1
x # -1/4
x..............|-inf..........-1/4..........+inf
4x + 1......|........(-)......o....(+)...........
Ineq........|........(-)......||.....(+)............
[tex]x \in ]-1/4 ; +\infty[[/tex]
-2x
------- < 0
x+8
-2x = 0 et x + 8 # 0
x = 0 et x # -8
x..........|-inf........-8.......0.........+inf
-2x......|.......(+)........(+)..o....(-).......
x + 8...|.......(-)....o...(+)........(+)......
Ineq....|.......(-)....||....(+).o....(-).......
[tex]x \in ]-\infty ; -8[ U ]0 ; +\infty[[/tex]
4x+4
-------- > 0
-5x-10
4x + 4 = 0 et -5x - 10 # 0
4x = -4 et 5x # -10
x = -4/4 et x # -10/5
x = -1 et x # -2
x..............|-inf........-2.......-1.........+inf
4x + 4.....|.......(-)........(-)...o....(+).......
-5x - 10...|.......(-)....o...(+)........(+)......
Ineq........|.......(+)....||...(-)..o....(+).......
[tex]x \in ]-\infty ; -2[ U ]-1 ; +\infty[[/tex]
3x+7
-------<0
5x+8
3x + 7 = 0 et 5x + 8 # 0
3x = -7 et 5x # -8
x = -7/3 et x # -8/5
x...............|-inf........-7/3.......-8/5.........+inf
3x + 7......|.......(-)......o...(+)...........(+)...........
5x + 8.....|.......(-)............(-)......o....(+)..........
Ineq........|.......(+)......o....(-).....||....(+).............
[tex]x \in ]-7/3 ; -8/5[[/tex]
