a) 25 chia hết cho n + 2

=> n + 2 ∈ Ư(25) 

=> n + 2 ∈ {1; -1; 5; -5; 25; -25}

=> n ∈ {-1; -3; 3; -7; 23; -27}  

b) 2n + 4 chia hết cho n - 1

=> (2n - 2) + 6 chia hết chi n - 1

=> 2(n - 1) + 6 chia hết cho n - 1

=> 6 chia hết cho n - 1

=> n - 1 ∈ Ư(6) = {1; -1; 2; -2; 3; -3; 6; -6}

=> n ∈ {2; 0; 3; -1; 4; -2; 7; -5} 

a) 25 ⋮ (n + 2)

⇒ n + 2 ∈ Ư(25) = {-25; -5; -1; 1; 5; 25}

⇒ n ∈ {-27; -7; -3; -1; 3; 23}

b) 2n + 4 = 2n - 2 + 6

= 2(n - 1) + 6

Để (2n + 4) ⋮ (n - 1) thì 6 ⋮ (n - 1)

⇒ n - 1 ∈ Ư(6) = {-6; -3; -2; -1; 1; 2; 3; 6}

⇒ n ∈ {-5; -2; -1; 0; 2; 3; 4; 7}

a) 10 ⋮ (x - 1)

⇒ x - 1 ∈ Ư(10) = {-10; -5; -2; -1; 1; 2; 5; 10}

⇒ x ∈ {-9; -4; -1; 0; 2; 3; 6; 11}

b) x + 5 = x - 2 + 7

Để (x - 5) ⋮ (x - 2) thì 7 ⋮ (x - 2)

⇒ x - 2 ∈ Ư(7) = {-7; -1; 1; 7}

⇒ x ∈ {-5; 1; 3; 9}

c) 3x + 8 = 3x - 3 + 11

= 3(x - 1) + 11

Để (3x + 8) ⋮ (x - 3) thì 11 ⋮ (x - 3)

⇒ x - 3 ∈ Ư(11) = {-11; -1; 1; 11}

⇒ x ∈ {-8; 2; 4; 14}

Bài 1:

1.

$\frac{1}{2}+\frac{3}{4}-\frac{4}{5}=\frac{5}{4}-\frac{4}{5}=\frac{9}{20}$

2.

$=(\frac{4}{29}.\frac{3}{13}+\frac{3}{13}.\frac{25}{29})+(\frac{-19}{26}+\frac{-7}{26})$

$=\frac{87}{29.13}+(-1)$

$=\frac{3}{13}-1=\frac{-10}{13}$

Bài 2:

a. 

$x=\frac{-7}{8}.\frac{4}{21}-\frac{2}{3}=\frac{-5}{6}$
b.

$\frac{1}{4}x=0,2-\frac{3}{4}=\frac{-11}{20}$

$x=\frac{-11}{20}:\frac{1}{4}=\frac{-11}{5}$

(3x+1).9-74=16

(3x+1).9=16+74

(3x+1).9=90

(3x+1)=90/9

3x+1=10

3x=9

x=3

`x-18-(6320:1580,25) = 300`

`=> x-18-(6320:1580,25) = 300`

`=> x - 25280/6321 = 300 + 18`

`=> x - 25280/6321 = 318`

`=> x = 25280/6321 + 318`

Do `25280/6321 ∉ N, 318 ∈ N`

`=> 25280/6321 + 318 ∉ N`

Hay `x ∉ N`

Vậy không tồn tại số tự nhiên `x` thỏa mãn `ycbt`

`430 + 35,2 = (x-9) . 25`

`=> 430 + 35,2 = (x-9) . 25`

`=> 465,2 = (x-9) . 25`

`=> x - 9 =  465,2  : 25`

`=> x - 9 = 2326/125`

`=> x = 2326/125 + 9`

Do `9 ∈ N, 2326/125 ∉ N`

`=> 2326/125 + 9 ∉ N`

Hay `x ∉ N`

Vậy không tồn tại số tự nhiên `x` thỏa mãn ycbt

`(42 . 43 + 43 . 57 + 43) - 360 : 4 `

`= 43 . (42 + 57 + 1) - 90`

`= 43 . 100 - 90`

`= 4300 - 90 `

`= 4210`

`372 - 19 . 4 + (981:9-13)`

`= 372 - 76 + (109-13)`

`= 296 + 96`

`= 392`

\(7\cdot4^{x-1}+4^{x+1}=23\)

=>\(7\cdot4^x\cdot\dfrac{1}{4}+4^x\cdot4=23\)

=>\(4^x\left(\dfrac{7}{4}+4\right)=23\)

=>\(4^x=23:\dfrac{23}{4}=4\)

=>x=1

\(119\times24-53\times23-24\times66\)

\(=\left(119-66\right)\times24-53\times23\)

\(=53\times24-53\times23\)

\(=53\times\left(24-23\right)\)

\(=53\times1\)

\(=53\)

\(119\cdot24-53\cdot23-24\cdot66\)

\(=24\left(119-66\right)-53\cdot23\)

\(=53\cdot24-53\cdot23=53\)

''_''  là sao vậy ?

\(\left[184:\left(96-124:31\right)-2\right].3651\)

\(=\left[184:\left(96-4\right)-2\right].3651\)

\(=\left[184:92-2\right].3651\)

\(=\left[2-2\right].3651\)

\(=0.3651\)

`= 3651`