Question

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

Answer 1

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

    3/2      -1

 

1. jeśli x ∈ (-oo, -1) to -(2x - 3) = -(x + 1) + x - 4

                                     -2x + 3 = -x - 1 + x - 4

                                      -2x + 3 = -5

                                       -2x = -5 - 3

                                        -2x = -8

                                           x = 4 ∉ (-oo, -1)

 

2. jesli x ∈ <-1, 3/2> to  -(2x - 3) = x + 1 + x - 4

                                      -2x + 3 = 2x  - 3

                                       -2x - 2x = -3 - 3

                                           -4x = -6

                                              x = 3/2 ∈ <-1, 3/2>

 

3. jesli x ∈ (3/2, + oo) to    2x - 3 = x + 1 + x - 4

                                          2x - 3 = 2x - 3

                                               0 = 0

                                               x ∈ R i  x ∈ (3/2, +oo)

                                                   x ∈ (3/2, + oo)

 

odp. x ∈ <3/2, + oo)