Question

2|x|-|x+1|=2 jak to dokładnie rozwiazac krok po kroku? w odpowiedziach pisze ze wynikiem bedzie -1 lub 3 skad to sie wzielo?

Answer 1

2|x| - |x + 1| = 2

  0          -1

 

1. x ∈ (-oo, -1> ⇒ (-2x) - [ -(x + 1) ] = 2

                         -2x + x + 1 = 2

                          -x = 2 - 1

                           -x = 1

                              x = -1 ∈ (-oo, -1>

 

2. x  ∈ (-1, 0> ⇒  -2x -(x + 1)  = 2

                            -2x - x - 1 = 2

                              -3x = 2 + 1

                              -3x = 3

                               x = -1 ∉ (-1, 0>

3. x ∈ (0, +oo) ⇒  2x - (x + 1 )= 2

                             2x - x - 1 = 2

                              x = 3 ∈ (0, +oo)

                                                   

odp. x = -1   i   x = 3