Question

Gasiti valorile lui x€Z pentru care (x+4) | (3x + 7)

Answer 1

(x+4)|(3x+7)     

(x+4)|(x+4)    <=>   (x+4)| 3 * (x+4)   <=> (x+4)| 3x+12
                                                                 (x+4)| 3x+7

===> (x+4)| 3x+12-3x-7
         (x+4)|5                      ====> x+4 ∈ { -/+ 1; -/+ 5}

1) x+4= 1 ==> x= -3
2) x+4=-1 ==> x= -5
3) x+4= 5 ==> x= 1
4) x+4=-5 ==> x=-9
x ∈ Z

Multimea solutiilor este : S ∈ { -9; -5; -3;1}