1.     Giải:

Do \(5x+13B\in\left(2x+1\right)\Rightarrow5x+13⋮2x+1.\)

 \(\Rightarrow2\left(5x+13\right)⋮2x+1\Rightarrow10x+26⋮2x+1.\)

 \(\Rightarrow5\left(2x+1\right)+21⋮2x+1.\)

Do 5(2x+1)⋮2x+1⇒ Ta cần 21⋮2x+1.

⇒ 2x+1 ϵ B(21)=\(\left\{1;3;7;21\right\}.\)

Ta có bảng:

Vậy xϵ\(\left\{0;1;3;10\right\}.\)

2. Giải:

Do (2x-18).(3x+12)=0.

⇒ 2x-18=0             hoặc             3x+12=0.

⇒ 2x     =18                               3x       =-12.

⇒   x     =9                                   x       =-4.

Vậy xϵ\(\left\{-4;9\right\}.\)

3. S= 1-2-3+4+5-6-7+8+...+2021-2022-2023+2024+2025.

S= (1-2-3+4)+(5-6-7+8)+...+(2021-2022-2023+2024)+2025 Có 506 cặp.

S= 0 + 0 + ... + 0 + 2025.

⇒S= 2025.

Tìm số nguyên x, biết:
1) -16 + 23 + x = - 16

7+x=-16

    x=-16-7

    x=-23
2) 2x – 35 = 15

2x=15+35

2x=50

  x=50:2

  x=25
3) 3x + 17 = 12

3x=12-17

3x=-5

  x=-5/3
4) (2x – 5) + 17 = 6

2x-5=6-17

2x-5=-11

2x=-11+5

2x=-6

  x=-6:2

  x=-3
5) 10 – 2(4 – 3x) = -4

2(4-3x)=10-(-4)

2(4-3x)=14

4-3x=14:2

4-3x=7

3x=4-7

3x=-3

  x=-3:3

  x=-1
6) - 12 + 3(-x + 7) = -18

3(-x+7)=-18-(-12)

3(x+7)=-6

x+7=-6:3

x+7=-2

    x=-2-7

    x=-9

tự đi mà làm

a, 7\(x\).(\(x\) - 10) = 0

   \(\left[{}\begin{matrix}7x=0\\x-10=0\end{matrix}\right.\)

    \(\left[{}\begin{matrix}x=0\\x=10\end{matrix}\right.\)

Vậy \(x\in\) {0; 10}

b, 17.(3\(x\) - 6).(2\(x\) - 18) = 0

    \(\left[{}\begin{matrix}3x-6=0\\2x-18=0\end{matrix}\right.\)

    \(\left[{}\begin{matrix}3x=6\\2x-18=0\end{matrix}\right.\)

     \(\left[{}\begin{matrix}x=6:3\\x=18:2\end{matrix}\right.\)

       \(\left[{}\begin{matrix}x=2\\x=9\end{matrix}\right.\)

c, (4 - 2\(x\)).(\(x\) - 3) = 0

    \(\left[{}\begin{matrix}4-2x=0\\x-3=0\end{matrix}\right.\)

    \(\left[{}\begin{matrix}2x=4\\x=3\end{matrix}\right.\)

    \(\left[{}\begin{matrix}x=4:2\\x=3\end{matrix}\right.\)

     \(\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)

    Vậy \(x\in\) {2; 3}

a) 22 + (2x -13) = 83 => 2x -13 = 61 => x = 37.

b) 51 - (-12 + 3x) = 27 => 63 - 3x = 27 => x = 12.

c) - (2x + 2) + 21 = - 23 => 2x + 2 = 44 => x = 21.

d) 25 - (25 - x) = 0 => 25 - 25 + x = 0 => x = 0.