Question

Resolvam em R as inequações:

a) (x+1).(x-1).(x-3) > 0
b) (2x-1).(-x+3).(-x+1) > 0

Answer 1

a)
                                _______-1___0___+1________+3_______
|           x + 1            |- - - - - - -| ++++++++|+++++++++|+++++++
|           x - 1             |- - - - - - -|- - - - - - - - |+++++++++|+++++++
|           x - 3             |- - - - - - -|- - - - - - - - |- - - - - - - - -|+++++++
| (x + 1)(x -1)(x - 3)  |- - - - - - -|++++++++ |- - - - - - - - -|+++++++
                             V = { x ∈ R /  -1  <  x < +1  ∨   x > 3}
b)
                                ________  0___1/2 ___1________3___________
|                2x - 1             |- - - - - - - - - -|++++|++++++++|++++++++
|               -x + 3              |++++++++++|++++|++++++++|- - - - - - - -
|               -x + 1              |++++++++++|++++|- - - - - - - -|- - - - - - - -
|(2x  - 1)(-x + 3)(-x + 1)   | - - - - - - - - - |++++|- - - - - - - -|+++++++++
                           V = { x ∈ r /  1/2  <  x  < 1    ∨    x > 3}