a)|x-3|=5
x-3=5=>x=5+3=8
x-3=-5=>x=-5+3=-2
[tex] = > x_{1} = - 2 \\ \\ \: \: \: \: \: \: \: \: \: x_{2} = 8[/tex]
b)||x-3|-3|=5
|x-3|-3=5
|x-3|-3=-5
|x-3|=5+3=8
x-3=8=>x=11
x-3=-8=>x=-5
|x-3|=-5+3=-2=>x € ∅
[tex] = > x_{1} = - 5 \\ \\ \: \: \: \: \: \: \: x_{2} = 11 [/tex]
c)|||x-3|-3|-3|=5
||x-3|-3|=5
||x-3|-3|=-5
||x-3|-3|=5+3=8
|x-3|-3=8=>x=14,x=-8
|x-3|-3=-8=>x € ∅
||x-3|-3|=-5+3=-2=>x € ∅
[tex] = > x_{1} = - 8 \\ \\ \: \: \: \: \: \: \: \: x_{2} = 14 [/tex]