Question

Rezolvati in Z ecuatiile.
|x-1|=2
|2x-6|=0
||x-3|-5|=4
|-x|=3

Answer 1

1)|x-1|=2=>
x-1=2 sau x-1=-2
x=2+1 x=-2+1
x=3 x=-1
Deci x poate fi :{-1;3}
2)|2x-6|=0=>
2x-6=0
2x=6
x=6:2
x=3

3)||x-3|-5|=4=> |x-3|-5=4(1) sau |x-3|-5=-4(2)

In relatia (1):
|x-3|-5=4=>|x-3|=4+5
|x-3|=9
Acum ai 2 variante
x-3=9 sau x-3=-9
x=9+3 x=-9+3
x=12 x=-6

In relatia (2):|x-3|-5=-4
|x-3|=-4+5
|x-3|=1
Acum ai 2 variante:
x-3=1 sau x-3=-1
x=1+3 x=-1+3
x=4 x=2
Deci x poate fi:{-6;2;4;12}

4)|-x|=3=>-x=3 sau -x=-3
x=-3 x=3
Deci x poate fi :{-3;3}