\(a.\)
Để \(6⋮\left(x-1\right)\)
\(\Leftrightarrow\left(x-1\right)\in\text{Ư}\left(6\right)\in\left\{1;2;3;6\right\}\)
\(\Rightarrow x\in\left\{2;3;4;7\right\}\)
\(b.\)
Để \(14⋮\left(2x+3\right)\)
\(\Leftrightarrow\left(2x+3\right)\in\text{Ư}\left(14\right)\in\left\{1;2;7;14\right\}\)
\(\Rightarrow x\in\left\{-1;-\dfrac{1}{2};2;\dfrac{11}{2}\right\}\)
Mà \(x\in N\Rightarrow x=2\)
\(c.\)
Ta có : \(2\left(x+1\right)=2x+2\)
Để \(10⋮\left(2x+2\right)\)
\(\Leftrightarrow\left(2x+2\right)\in\text{Ư}\left(10\right)\in\left\{1;2;5;10\right\}\)
\(\Rightarrow x\in\left\{-\dfrac{1}{2};0;\dfrac{3}{2};4\right\}\)
Mà \(x\in N\Rightarrow x\in\left\{0;4\right\}\)
