Question

tìm số nguyên x, biết: a) (x+13) chia hết cho (x+8), b) (3x+2) chia hết cho (x-3), c) 3x +9 chia hết cho 2x+1

Answer 1

a: \(x+13⋮x+8\)

=>\(x+8+5⋮x+8\)

=>\(5⋮x+8\)

=>\(x+8\in\left\{1;-1;5;-5\right\}\)

=>\(x\in\left\{-7;-9;-3;-13\right\}\)

b:\(3x+2⋮x-3\)

=>\(3x-9+11⋮x-3\)

=>\(11⋮x-3\)

=>\(x-3\in\left\{1;-1;11;-11\right\}\)

=>\(x\in\left\{4;2;14;-8\right\}\)

c: \(3x+9⋮2x+1\)

=>\(6x+18⋮2x+1\)

=>\(6x+3+15⋮2x+1\)

=>\(15⋮2x+1\)

=>\(2x+1\in\left\{1;-1;3;-3;5;-5;15;-15\right\}\)

=>\(2x\in\left\{0;-2;2;-4;4;-6;14;-16\right\}\)

=>\(x\in\left\{0;-1;1;-2;2;-3;7;-8\right\}\)