Question

| x + 3 | = | x | - x

Answer 1

 |x + 3| = |x | - x

      -3         0

 

1. jesli x ∈ (-oo, - 3) ⇒ -(x + 3) = -x - x

                                     -x - 3 = -2x

                                     -x + 2x = 3

                                        x = 3  ∉ (-oo, - 3)

 

2. jesli x ∈ <-3, 0> ⇒ (x + 3) = -x - x

                                  x + 3 = -2x

                                  x + 2x = -3

                                   3x = -3

                                     x = -1 ∈ <-3, 0>

 

3. jesli x ∈ (0, +oo) ⇒ (x + 3) = x - x

                                     x + 3 = 0

                                      x = -3 ∉ (0, +oo)

odp. x = -1

Answer 2

|x|=x , gdy x≥0

|x|=-x, gdy x<0

Mamy 2 wyrazenia w wartosci bezwzglednej, z miejscami zerowymi -3 lub 0

Nalezy rozpatrzyc III przypadki tego rownania

1. gdy x<-3

-(x+3)=-x-x

-x-3=-x-x

-x+2x=3

x=3∉D

2. gdy  -3≤ x < 0

x+3=-x-x

x+2x=-3

3x=-3

x=-1

3. gdy x≥0

x+3=x-x

x+3=0

x=-3 ∉ D

 

Odp. x=-1