Question

3n-7⋮2n-3

Answer 1

\(3n-7⋮2n-3\)

=>\(6n-14⋮2n-3\)

=>\(6n-9-5⋮2n-3\)

=>\(-5⋮2n-3\)

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

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

=>\(n\in\left\{2;1;4;-1\right\}\)

Answer 2

\(3n-7⋮2n-3\)

\(\Rightarrow2\left(3n-7\right)-3\left(2n-3\right)⋮2n-3\)

\(\Rightarrow\left(6n-14\right)-\left(6n-9\right)⋮\left(2n-3\right)\)

\(\Rightarrow6n-14-6n+9⋮\left(2n-3\right)\)

\(\Rightarrow-5⋮\left(2n-3\right)\) 

\(\Rightarrow2n-3\inƯ\left(-5\right)=\left\{1;-1;5;-5\right\}\)

Ta có bảng giá trị:

Vậy \(n\in\left\{2;1;4;-1\right\}\)