Răspuns:
x ∈ {-7; 2; 3; 12}
Explicație pas cu pas:
[tex](2x-5) | (3x+2) < = > \frac{3x + 2}{2x - 5} [/tex]
[tex]2 \times (3x+2) = 6x + 4 \\ 3\times (2x-5) = 6x - 15 \\ (6x + 4) - (6x - 15) = 19[/tex]
=> d ∈ Z, d ∈ {-19; -1; 1; 19}
=> (2x - 5) ∈ {-19; -1; 1; 19}
[tex]d=-19=> 2x - 5 = -19\\ 2x = -19 + 5 \\ 2x = -14 = > x = -7[/tex]
[tex]d=-1=> 2x - 5 = -1 \\ 2x = - 1 + 5 \\ 2x = 4 = > x = 2[/tex]
[tex]d=1=> 2x - 5 = 1 \\ 2x = 1 + 5 \\ 2x = 6 = > x = 3[/tex]
[tex]d=19=> 2x - 5 = 19 \\ 2x = 19 + 5 \\ 2x = 24 = > x = 12[/tex]
=> soluție x ∈ {-7; 2; 3; 12}
