Những hành vi vi phạm pháp luật về chỗ ở của công dân là :

- Tự ý vào chỗ ở của người khác khi chưa được sự đồng ý của họ .

- Tự ý vào nhà người khác khi vắng chủ .

- Tiến hành khám xét chỗ ở không đúng quy định pháp luật .

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Gọi A = 1 - 3 + 3² - 3³ + 3⁴ - ... - 3²⁰¹⁷

3A = 3.( 1 - 3 + 3² - 3³ + 3⁴ - ... - 3²⁰¹⁷)

3A = 3 - 3² + 3³ - 3⁴ + ... + 3²⁰¹⁸

3A + A = ( 3 - 3² + 3³ - 3⁴ + ... + 3²⁰¹⁸ ) + ( 1 - 3 + 3² - 3³ + 3⁴ - ... - 3²⁰¹⁷)

4A = 1 + [ 3 - 3 ] + [ ( - 3² ) + 3² ] + ...+ [ 3²⁰¹⁷ - 3²⁰¹⁷ ] + 3²⁰¹⁸

4A = 1 + 3²⁰¹⁸

A = \(\dfrac{1+3^{2018}}{4}\)

4a + 5b + 7c \(⋮\) 11

=> 4.( 4a + 5b + 7c ) \(⋮\) 11

=> 16a + 20b + 28c \(⋮\) 11

=> ( 5a + 11a ) + ( 9b + 11b ) + ( 6c + 22c ) \(⋮\) 11

=> 5a + 11a + 9b + 11b + 6c + 22c \(⋮\) 11

=> ( 5a + 6b + 6c ) + ( 11a + 11b + 22c ) \(⋮\) 11

11a + 11b + 22c \(⋮\) 11 vì 11a \(⋮\) 11 ; 11b \(⋮\) 11 ; 22c \(⋮\) 11

=> 5a + 6b + 6c \(⋮\) 11 .

x⁴ - 2x³ - x + 7 chia hết cho x - 3

= x.(x³ - 2.x² - 1 ) + 7 chia hết cho x - 3

= x.[x².(x - 2 - 1 )] + 7 chia hết cho x - 3

= x.x².(x - 3) + 7 chia hết cho x - 3

Vì x.x².(x - 3) chia hết cho x - 3 nên 7 chia hết cho x - 3 .

=> x - 3 \(\in\) Ư(7)

Ư(7) = {1;-1;7;-7}

=> x - 3 \(\in\) {1;-1;7;-7}

=> x \(\in\) {4;2;10;-4}.

Đặt :

\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{2016}}\)

\(\dfrac{1}{3}A=\dfrac{1}{3}.\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{2016}}\right)\)

\(\dfrac{1}{3}A=\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{2017}}\)

\(\dfrac{1}{3}A-A=\left(\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{2017}}\right)-\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{2016}}\right)\)

\(-\dfrac{2}{3}A=\dfrac{1}{3^{2017}}-\dfrac{1}{3}\)

\(A=\dfrac{\dfrac{1}{3^{2017}}-\dfrac{1}{3}}{-\dfrac{2}{3}}\).

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left(\dfrac{131313}{151515}+\dfrac{131313}{353535}+\dfrac{131313}{636363}+\dfrac{131313}{999999}\right)=-5\)

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left(\dfrac{13}{15}+\dfrac{13}{35}+\dfrac{13}{63}+\dfrac{13}{99}\right)=-5\)

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left(\dfrac{13}{3.5}+\dfrac{13}{5.7}+\dfrac{13}{7.9}+\dfrac{13}{9.11}\right)=-5\)

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left[\dfrac{13}{2}.\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}\right)\right]=-5\)

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left[\dfrac{13}{2}.\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\right)\right]=-5\)

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left[\dfrac{13}{2}.\left(\dfrac{1}{3}-\dfrac{1}{11}\right)\right]=-5\)

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left[\dfrac{13}{2}.\dfrac{8}{33}\right]=-5\)

\(\dfrac{2}{3}x-\dfrac{700}{11}:\dfrac{52}{33}=-5\)

\(\dfrac{2}{3}x-\dfrac{525}{13}=-5\)

\(\dfrac{2}{3}x=-5+\dfrac{525}{13}=\dfrac{460}{13}\)

\(x\) = \(\dfrac{460}{13}:\dfrac{2}{3}=\dfrac{690}{13}\).

\(\dfrac{2}{7}=\dfrac{8}{28}=\dfrac{1}{28}+\dfrac{1}{4}\).

Bài 1 :

a) 0,5x - \(\dfrac{2}{3}x=\dfrac{7}{12}\)

\(\dfrac{1}{2}x-\dfrac{2}{3}x=\dfrac{7}{12}\)

\(x.\left(\dfrac{1}{2}-\dfrac{2}{3}\right)\)= \(\dfrac{7}{12}\)

\(x.\dfrac{-1}{6}=\dfrac{7}{12}\)

\(x=\dfrac{7}{12}:\dfrac{-1}{6}\)

x = \(\dfrac{-7}{2}\).

b) \(x:4\dfrac{1}{3}=-2,5\)

\(x:\dfrac{13}{3}=\dfrac{-5}{2}\)

\(x=\dfrac{-5}{2}.\dfrac{13}{3}\)

\(x=\dfrac{-15}{26}\).

c) \(\left(\dfrac{3x}{7}+1\right):\left(-4\right)=\dfrac{-1}{28}\)

\(\dfrac{3x}{7}+1=\dfrac{-1}{28}.\left(-4\right)\)

\(\dfrac{3x}{7}+1=\dfrac{1}{7}\)

\(\dfrac{3x}{7}=\dfrac{1}{7}-1\)

\(\dfrac{3x}{7}=\dfrac{-6}{7}\)

=> 3x = -6

x = -6 :3 = -2.

Bài 2 : Bài giải :

Đổi \(26\dfrac{1}{4}\)km/h = 26,25 km/h .

Độ dài quãng đường AB là :

26,25 . 2,4 = 63 (km)

Thời gian người ấy đi từ B đến A là :

63 : 30 = 2,1 ( giờ) = 2 giờ 6 phút .

Bài 3 :

\(4\dfrac{3}{4}+\left(-0,37\right)+\dfrac{1}{8}+\left(-1,28\right)+\left(-2,5\right)+3\dfrac{1}{12}\)

= \(\dfrac{19}{4}+\dfrac{-37}{100}+\dfrac{1}{8}+\dfrac{-32}{25}+\dfrac{-5}{2}+\dfrac{37}{12}\)

= \(\left(\dfrac{19}{4}+\dfrac{1}{8}+\dfrac{-5}{2}\right)+\left(\dfrac{-37}{100}+\dfrac{-32}{25}\right)+\dfrac{37}{12}\)

= \(\dfrac{19}{8}+\dfrac{-33}{20}+\dfrac{37}{12}\)

= \(\dfrac{457}{120}\)

= \(3\dfrac{97}{120}\).