Tìm số nguyên x biết: a) 6 $\vdots$ ( x + 2 ) b) ( x + 13 ) $\vdots$ ( x + 8 ) c) ( 3x + 2 ) $\vdots$ ( x - 3 ) d) 3x + 9 $\vdots$ 2x + 1

`6`$\vdots$`(x+2)`

`=>x+2in Ư(6)={+-1;+-2;+-3;+-6}`

Ta có bảng sau:

\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline \text{$x+2$}&\text{1}&\text{$-1$}&\text{2}&\text{$-2$}&\text{3}&\text{$-3$}&\text{6}&\text{$-6$}\\\hline \text{$x$}&\text{$-1$}&\text{$-3$}&\text{0}&\text{$-4$}&\text{1}&\text{$-5$}&\text{$4$}&\text{$-8$}\\\hline\end{array}

Vậy `x in {-1;-3;0;-4;1;-5;4;-8}`

`b)(x+13)`$\vdots$`(x+8)`

`=>[(x+13)-(x+8)]`$\vdots$`(x+8)`

`=>[x+13-x-8]`$\vdots$`(x+8)`

`=>5`$\vdots$`(x+8)`

`=>x+8 in Ư(5)={+-1;+-5}`

Ta có bảng sau:

\begin{array}{|c|c|c|c|c|}\hline \text{$x+8$}&\text{1}&\text{$-1$}&\text{5}&\text{$-5$}\\\hline \text{$x$}&\text{$-7$}&\text{$-9$}&\text{$-3$}&\text{$-13$}\\\hline\end{array}

Vậy `x in {-7;-9;-3;-13}`

`c)(3x+2)`$\vdots$`(x-3)`

`=>[(3x+2)-3(x-3)]`$\vdots$`(x-3)`

`=>[3x+2-3x+9]`$\vdots$`(x-3)`

`=>11`$\vdots$`(x-3)`

`=>x-3 in Ư(11)={+-1;+-11}`

Ta có bảng sau:

\begin{array}{|c|c|c|c|c|}\hline \text{$x-3$}&\text{1}&\text{$-1$}&\text{11}&\text{$-11$}\\\hline \text{$x$}&\text{$4$}&\text{$2$}&\text{$14$}&\text{$-8$}\\\hline\end{array}

Vậy `x in {4;2;14;-8}`

`d)3x+9`$\vdots$`2x+1`

`=>2(3x+9)-3(2x+1)`$\vdots$`2x+1`

`=>6x+18-6x-3`$\vdots$`2x+1`

`=>15`$\vdots$`2x+1`

`=>2x+1 in Ư(15)={+-1;+-3;+-5;+-15}`

Ta có bảng sau:

\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline \text{$2x+1$}&\text{1}&\text{$-1$}&\text{3}&\text{$-3$}&\text{5}&\text{$-5$}&\text{$15$}&\text{$-15$}\\\hline \text{$2x$}&\text{0}&\text{$-2$}&\text{2}&\text{$-4$}&\text{4}&\text{$-6$}&\text{$14$}&\text{$-16$}\\\hline \text{$x$}&\text{0}&\text{$-1$}&\text{1}&\text{$-2$}&\text{2}&\text{$-3$}&\text{$7$}&\text{$-8$}\\\hline\end{array}

Vậy `x in {0;-1;1;-2;2;-3;7;-8}`

Đáp án:

 Xin hay nhất cho nhóm ạ!

Giải thích các bước giải:

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