25 - (30 + x) = x - (27 - 8)

25 - 30 - x = x - 27 + 8

- x - x = -25 + 30 - 27 + 8

-2x = -14

x = -14 : (-2)

x = 7.

\(\frac{2}{x}=\frac{y}{15}=\frac{\left(-25\right)}{75}\)

\(\Rightarrow\frac{y}{15}=\frac{\left(-1\right)}{3}\)

\(\frac{y}{15}=\frac{\left(-5\right)}{15}\)

\(\Rightarrow15y=15\times\left(-5\right)\)

\(15y=\left(-75\right)\)

\(y=\left(-75\right)\div15\)

\(y=\left(-5\right)\)

\(\Rightarrow\frac{2}{x}=\frac{\left(-5\right)}{15}\)

\(\frac{2}{x}=\frac{\left(-1\right)}{3}\)

\(\Rightarrow-x=3\times2\)

\(-x=6\)

\(x=\left(-6\right)\)

\(V\text{ậy}x=\left(-6\right);y=\left(-5\right)\)

|x + 2| - 13 = -1

=> |x + 2| = -1 + 13

=> |x + 2| = 12

=> \(\orbr{\begin{cases}x+2=12\\x+2=-12\end{cases}}\)

=> \(\orbr{\begin{cases}x=10\\x=-14\end{cases}}\)

x - (17 - x) = -7

=> x - 17  +x = -7

=> 2x - 17 = -7

=> 2x = -7 + 17

=> 2x = 10

=> x = 5

10(x + 7) - 8(x + 5) = 6(-5) + 24

=> 10x + 70 - 8x - 40 = -30 + 24

=> 2x + 30 = -6

=> 2x = -6 - 30

=> 2x = -36

=> x = -18

\(A=\frac{n+3}{n-2}=\frac{n-2+5}{n-2}=1+\frac{5}{n-2}\)

Để A nguyên khi \(\frac{5}{n+2}\inℤ\Rightarrow n+2\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

Đây là phần làm

Vì 12 : 6 = 2 nên 5.2 = 10 . Vậy X = 10

\(\frac{A}{3}=\frac{4-1}{1.4}+\frac{7-4}{4.7}+...+\frac{91-91}{91.94}\)

\(\frac{A}{3}=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{91}-\frac{1}{94}=1-\frac{1}{94}=\frac{93}{94}\Rightarrow A=\frac{3.93}{94}\)

Đặt ƯCLN ( 14n + 3 , 21n + 4 ) = d ( d \(\inℕ^∗\))

\(14n+3⋮d\Rightarrow42n+9⋮d\)(1)

\(21n+4⋮d\Rightarrow42n+8⋮d\)(2)

Lấy (1) - (2) ta được : \(42n+9-42n-8⋮d\Rightarrow1⋮d\Rightarrow d=1\)

Vậy ta có đpcm 

\(A=\frac{3n+2}{n}=3+\frac{2}{n}\)

A nguyên \(\Leftrightarrow3+\frac{2}{n}\)nguyên \(\Leftrightarrow\frac{2}{n}\)nguyên
\(\Leftrightarrow n\inƯ\left(2\right)\in\left\{\pm1;\pm2\right\}\in Z\)

Vậy \(n\in\left\{\pm1;\pm2\right\}\)thì A nguyên

Trả lời:

ta cần tìm n để (3n+2) mod n =0

Ta thấy: 3n mod n =0

=> để A nguyên thì

2 mod n =0

=> n={-2,-1,1,2}