Bài 2:

a: \(x-\dfrac{1}{2}=\dfrac{7}{13}\cdot\dfrac{13}{28}\)

=>\(x-\dfrac{1}{2}=\dfrac{7}{28}=\dfrac{1}{4}\)

=>\(x=\dfrac{1}{4}+\dfrac{1}{2}=\dfrac{3}{4}\)

b: \(\dfrac{x}{15}=\dfrac{-3}{11}\cdot\dfrac{77}{36}\)

=>\(\dfrac{x}{15}=\dfrac{-3}{36}\cdot\dfrac{77}{11}=7\cdot\dfrac{-1}{12}=-\dfrac{7}{12}\)

=>\(x=-\dfrac{7}{12}\cdot15=-\dfrac{105}{12}=-\dfrac{35}{4}\)

c: \(x:\dfrac{15}{11}=\dfrac{-3}{12}:8\)

=>\(x:\dfrac{15}{11}=-\dfrac{1}{4}:8=-\dfrac{1}{32}\)

=>\(x=-\dfrac{1}{32}\cdot\dfrac{15}{11}=\dfrac{-15}{352}\)

Bài 1:

a: \(\dfrac{-12}{25}\cdot\dfrac{10}{9}=\dfrac{-12}{9}\cdot\dfrac{10}{25}=\dfrac{-4}{3}\cdot\dfrac{2}{5}=\dfrac{-8}{15}\)

b: \(\dfrac{10}{21}-\dfrac{3}{8}\cdot\dfrac{4}{5}\)

\(=\dfrac{10}{21}-\dfrac{12}{40}\)

\(=\dfrac{10}{21}-\dfrac{3}{10}=\dfrac{100-63}{210}=\dfrac{37}{210}\)

c: \(\dfrac{28}{11}:\dfrac{21}{22}\cdot9=\dfrac{28}{11}\cdot\dfrac{22}{21}\cdot9\)

\(=\dfrac{28}{21}\cdot\dfrac{22}{11}\cdot9=\dfrac{4}{3}\cdot2\cdot9=\dfrac{4}{3}\cdot18=24\)

d: \(-\dfrac{10}{21}\cdot\left[\dfrac{9}{15}+\left(\dfrac{3}{5}\right)^2\right]\)

\(=\dfrac{-10}{21}\cdot\left[\dfrac{3}{5}+\dfrac{9}{25}\right]\)

\(=\dfrac{-10}{21}\cdot\dfrac{15+9}{25}\)

\(=\dfrac{-10}{25}\cdot\dfrac{24}{21}=\dfrac{-2}{5}\cdot\dfrac{8}{7}=\dfrac{-16}{35}\)

e: \(\left(\dfrac{2}{3}-\dfrac{1}{2}-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{4}-\dfrac{1}{7}\right)\)

\(=\left(\dfrac{1}{3}-\dfrac{1}{2}\right)\cdot\dfrac{28-7-4}{28}\)

\(=\dfrac{-1}{6}\cdot\dfrac{17}{28}=\dfrac{-17}{168}\)

f: \(\left(\dfrac{15}{21}:\dfrac{5}{7}\right):\left(\dfrac{6}{5}:2\right)\)

\(=\left(\dfrac{5}{7}\cdot\dfrac{7}{5}\right):\left(\dfrac{6}{5\cdot2}\right)\)

\(=1:\dfrac{6}{10}=\dfrac{10}{6}=\dfrac{5}{3}\)

Bài 4: 

Số thứ hai là 150x3/5=90

Số thứ ba là 90x2/3=60

Số thứ tư là 60x7/10=42

Trung bình của bốn số là:
(150+90+60+42):4=85,5

\(d,\dfrac{-25}{12}-\left(\dfrac{23}{12}+1\dfrac{1}{2}\right)=d,\left(\dfrac{-25}{12}-\dfrac{23}{12}\right)-\dfrac{3}{2}=\dfrac{-48}{12}-\dfrac{3}{2}=-4-\dfrac{3}{2}=\dfrac{-8}{2}-\dfrac{3}{2}=-\dfrac{11}{2}\\ e,\dfrac{-1}{9}.\dfrac{-3}{5}-\dfrac{5}{6}.\dfrac{3}{-5}+\dfrac{-5}{2}.\dfrac{3}{5}=\dfrac{1}{9}.\dfrac{3}{5}+\dfrac{5}{6}.\dfrac{3}{5}-\dfrac{5}{2}.\dfrac{3}{5}=\dfrac{3}{5}\left(\dfrac{1}{9}+\dfrac{5}{6}-\dfrac{5}{2}\right)=\dfrac{3}{5}.\dfrac{-14}{9}=\dfrac{-14}{15}\)

\(\dfrac{1}{2^2}>\dfrac{1}{2\cdot3}=\dfrac{1}{2}-\dfrac{1}{3}\)

\(\dfrac{1}{3^2}>\dfrac{1}{3\cdot4}=\dfrac{1}{3}-\dfrac{1}{4}\)

...

\(\dfrac{1}{100^2}>\dfrac{1}{100\cdot101}=\dfrac{1}{100}-\dfrac{1}{101}\)

Do đó: \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{100^2}>\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{100}-\dfrac{1}{101}=\dfrac{1}{2}-\dfrac{1}{101}=\dfrac{99}{202}\)

\(\dfrac{1}{2^2}< \dfrac{1}{1\cdot2}=1-\dfrac{1}{2}\)

\(\dfrac{1}{3^2}< \dfrac{1}{2\cdot3}=\dfrac{1}{2}-\dfrac{1}{3}\)

...

\(\dfrac{1}{100^2}< \dfrac{1}{99\cdot100}=\dfrac{1}{99}-\dfrac{1}{100}\)

Do đó: \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{100^2}< 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}=1-\dfrac{1}{100}=\dfrac{99}{100}\)

Suy ra: \(\dfrac{9}{202}< \dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{100^2}< \dfrac{99}{100}\)

\(a)(-3/5)*x=-1/20+1/2=9/20=>x=9/20:(-3/5)=-3/4\)

Các câu kia làm tương tự nhé, chúc em học giỏi

a: =>-3/5x=-1/20+1/2=-1/20+10/20=-9/20

=>x=3/4

b: =>-1/15x-2/15=3/5

=>-1/15x=6/15+2/15=8/15

=>x=-8

c: \(\Leftrightarrow\left(2x-1\right)\left(x-3\right)\left(x+3\right)=0\)

hay \(x\in\left\{\dfrac{1}{2};3;-3\right\}\)

a, \(-\dfrac{3}{5}x=-\dfrac{1}{20}+\dfrac{1}{2}=\dfrac{9}{20}\Leftrightarrow x=-\dfrac{3}{4}\)

b, \(-\dfrac{2}{5}x+\dfrac{1}{3}x-\dfrac{28}{105}=\dfrac{3}{5}\Leftrightarrow-\dfrac{1}{15}x=\dfrac{13}{15}\Leftrightarrow x=-13\)

c, \(\left(\dfrac{1}{2}x-\dfrac{1}{4}\right)\left(x-3\right)\left(x+3\right)=0\Leftrightarrow x=\dfrac{3}{4};x=3;x=-3\)

a: \(\Leftrightarrow2n-2+3⋮n-1\)

\(\Leftrightarrow n-1\in\left\{1;-1;3;-3\right\}\)

hay \(n\in\left\{2;0;4;-2\right\}\)

b \(\Leftrightarrow12n-9⋮3n+1\)

\(\Leftrightarrow12n+4-13⋮3n+1\)

\(\Leftrightarrow3n+1\in\left\{1;-1;13;-13\right\}\)

hay \(n\in\left\{0;-\dfrac{2}{3};4;-\dfrac{14}{3}\right\}\)

c: \(\Leftrightarrow n\left(n-1\right)+1⋮n-1\)

\(\Leftrightarrow n-1\in\left\{1;-1\right\}\)

hay \(n\in\left\{2;0\right\}\)

Nhìn cứ giống toán lớp 8,9 hơn lớp 6 đúng hok

a, \(2\left(n-1\right)+3⋮n-1\Rightarrow3⋮n-1\Leftrightarrow n-1\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)

b, \(4n-3⋮3n+1\Leftrightarrow12n-9⋮3n+1\)

\(\Leftrightarrow4\left(3n+1\right)-13⋮3n+1\Rightarrow-13⋮3n+1\Rightarrow3n+1\inƯ\left(-13\right)=\left\{\pm1;\pm13\right\}\)

c, \(n^2-n+1=n\left(n-1\right)+1⋮n-1\Rightarrow n-1\inƯ\left(1\right)=\left\{\pm1\right\}\)

\(=\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{50}+\dfrac{1}{51}-\dfrac{102}{51\cdot52}\)

\(=\dfrac{1}{2}+\dfrac{1}{51}-\dfrac{102}{51\cdot52}\)

\(=\dfrac{1}{2}+\dfrac{52-102}{51\cdot52}=\dfrac{1}{2}+\dfrac{-50}{51\cdot52}=\dfrac{319}{663}\)

a: =>2x-3-3x+1=34

=>-x-2=34

=>-x=36

hay x=-36

b: =>x+1=0 hoặc 5-5x=0

=>x=-1 hoặc x=1

c: \(\Leftrightarrow\left(2x+1\right)^3=45+19=64\)

=>2x+1=4

=>2x=3

hay x=3/2

d: \(\Leftrightarrow4x^2=16\)

=>x=2 hoặc x=-2

a) \(\left(2x-3\right)+\left(-3x+1\right)=34\)

\(2x-3-3x+1=34\)

\(-x=36\)

\(x=-36\)

b) \(\left(x+1\right)\left(5-5x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=1\end{matrix}\right.\)

c) \(\left(2x+1\right)^3=49-\left(-19\right)=64=4^3\)

\(2x+1=4\)

\(x=\dfrac{3}{2}\)

d) \(4x^2-3=13\)

\(4x^2=16\)

\(x^2=4\)

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

a) \(\left(2x-3\right)\left(-3x+1\right)=34\)

\(\left[{}\begin{matrix}2x-3=34\\-3x+1=34\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{37}{2}\\x=-11\end{matrix}\right.\)

b) \(\left(x+1\right)\left(5-5x\right)=0\)

\(\left[{}\begin{matrix}x+1=0\\5-5x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x=-1\end{matrix}\right.\)

c) \(\left(2x+1\right)^3=45-\left(-19\right)\)

\(\left(2x+1\right)^3=64\)

\(\left(2x+1\right)^3=2^6\)

Bài 3:

\(a,\left(5x-2\right)+\left(-3x+1\right)=\left(-42\right)-\left(-91\right)\\ \Rightarrow5x-2+\left(-3x\right)+1=50\\ \Rightarrow2x-1=49\\ \Rightarrow2x=50\\ \Rightarrow x=25\\ b,\left(3-x\right)\left(9+3x\right)=0\\ \Rightarrow\left[{}\begin{matrix}3-x=0\\9+3x=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\3x=-9\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)

\(c,5x^2-\left(-6\right)=\left(-33\right)-\left(-44\right)\\ \Rightarrow5x^2+6=11\\ \Rightarrow5x^2=5\\ \Rightarrow x^2=1\\ \Rightarrow\left[{}\begin{matrix}x=-1\\x=1\end{matrix}\right.\)

\(d,2\left(2x-4\right)^2-77=-45\\ \Rightarrow2\left(2x-4\right)^2=32\\ \Rightarrow\left(2x-4\right)^2=16\\ \Rightarrow\left[{}\begin{matrix}2x-4=-4\\2x-4=4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=0\\2x=8\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)

bài 3

c] 5x mũ 2 -[-6] =[-33] - [-44]

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