Question

3. Scrieți sub formă de interval mulțimile de mai jos care satisfac relaţiile date:
a) A = {x € R | |x|<3};
b) B= {re R |||<4};
c) C= {x= R]||r+1]<2};
d) D= {xe R | |x-2| ≤5};
f) F= {xe R ||2x-1|≤5}.
e) E= {xe R ||2x +3|<7};

Answer 1

Răspuns:

a)A=?

|x|< 3=>-3<x< 3=>A=(-3;3)

c)C=?

|r+1|<2=>-2<r+1<2|-1 =>-3<r<1=>C=(-3;1)

d)D=?

|x-2|≤5=>-5≤x-2≤5|+2 =>-3≤x≤7=>D=[-3;7]

e)E=?

|2x+3|≤5=>-5≤2x+3≤5|-3 =>-8≤2x≤2|:2=>-4≤x≤1=>E=[-4;1]

f)F=?

|2x-1|≤5=>-5≤2x-1≤5|+1 =>-4≤2x≤6|:2 =>-2≤x≤3=>F=[-2;3]