bài 1 a)

\(\frac{15}{7}\times\frac43+\frac63\)

=\(\frac{60}{21}+\frac63\)

=\(\frac{60}{21}+\frac{42}{21}\)

=\(\frac{102}{21}\)

=\(\frac{34}{7}\)

b)\(\frac{-13}{41}\times\frac{17}{11}\times\frac{11}{17}\)

=\(\frac{-13}{41}\times\left(\frac{17}{11}\times\frac{11}{17}\right)\)

=\(\frac{-13}{41}\times1\)

=\(\frac{-13}{41}\)

Bài 1:

a) \(\frac{25}{4}+\frac{-5}{4}=\frac{25-5}{4}=\frac{20}{4}=5\)

b)\(\frac{-5}{9}+\left(\frac{-2}{7}\right)=\frac{-35}{63}+\left(\frac{-18}{63}\right)=\frac{-53}{63}\)

c) \(\frac{1}{4}+\frac{9}{11}+\frac{7}{4}+\left(\frac{-2}{11}\right)=\left(\frac{1}{4}+\frac{7}{4}\right)+\left(\frac{-2}{11}+\frac{9}{11}\right)=2+\frac{7}{11}=\frac{22+7}{11}=\frac{29}{11}\)

d) \(\frac{-5}{19}.\frac{8}{19}+\left(\frac{-14}{19}\right).\frac{11}{19}=\frac{-40}{361}-\frac{151}{361}=-\frac{191}{361}\)

Bài 2: 

a) \(x+\frac{5}{9}=\frac{-8}{9}\)  \(\Leftrightarrow x=\frac{-8}{9}-\frac{5}{9}\)  \(\Leftrightarrow x=-\frac{13}{9}\)

b) \(\frac{-1}{8}-x=\frac{9}{20}\)  \(\Leftrightarrow x=\frac{-1}{8}-\frac{9}{20}\)  \(\Leftrightarrow x=\frac{-5}{40}-\frac{18}{40}\)  \(\Leftrightarrow x=-\frac{23}{40}\)

c) (x + 5)³ - 12 = 15

\(\Leftrightarrow\)(x + 5)³ = 27

\(\Leftrightarrow\)x + 5 = 3

\(\Leftrightarrow\)x = -2

d) \(\left|x-3\right|-\frac{4}{15}=\frac{26}{15}\)  \(\Leftrightarrow\left|x-3\right|=2\)  \(\Leftrightarrow\orbr{\begin{cases}x-3=2\\x-3=-2\end{cases}}\)  \(\Leftrightarrow\orbr{\begin{cases}x=5\\x=1\end{cases}}\)

=>(5/17+12/17)+(-20/31-11/31)-4/9<=x/9<=(-3/7-4/7)+(7/15+8/15)+2/3

=>-4/9<=x/9<=6/9

=>-4<=x<=6

hay \(x\in\left\{-4;-3;-2;-1;0;...;6\right\}\)

a: x/5=32/80

nên x/5=2/5

hay x=2

13/x=26/30

nên 13/x=13/15

hay x=15

-x/7=22/-77

=>x/7=2/7

hay x=2

b: x/9=28/36

=>x/9=7/9

hay x=7

-10/x=50/55

=>-10/x=10/11

hay x=-11

a)

1) x/5 = 32/80

\(x : 5 = 32 : 80\) \(x = 5 \cdot \frac{32}{80}\) \(x = 5 \cdot \frac{2}{5}\) \(x = 2\)

2) 13/x = 26/30

\(13 : x = 26 : 30\) \(13 \cdot 30 = x \cdot 26\) \(390 = 26 x\) \(x = 390 : 26\) \(x = 15\)

3) -x/7 = 22/(-77)

\(- x : 7 = 22 : \left(\right. - 77 \left.\right)\) \(- x = 7 \cdot \frac{22}{- 77}\) \(- x = 7 \cdot \left(\right. - \frac{2}{7} \left.\right)\) \(- x = - 2\) \(x = 2\)

b)

1) x/9 = 28/36

\(x : 9 = 28 : 36\) \(x = 9 \cdot \frac{28}{36}\) \(x = 9 \cdot \frac{7}{9}\) \(x = 7\)

2) -10/x = 50/55

\(- 10 : x = 50 : 55\) \(- 10 \cdot 55 = 50 x\) \(- 550 = 50 x\) \(x = - 550 : 50\) \(x = - 11\)

3) 23/(-x) = 46/50

\(23 : \left(\right. - x \left.\right) = 46 : 50\) \(23 \cdot 50 = 46 \left(\right. - x \left.\right)\) \(1150 = - 46 x\) \(x = 1150 : \left(\right. - 46 \left.\right)\) \(x = - 25\)

✅ Kết quả cuối cùng

a)

1. x = 2
2. x = 15
3. x = 2

b)

1. x = 7
2. x = -11
3. x = -25

a/ \(\frac{x+2}{27}=\frac{x}{9}\)

=> 9(x + 2) = 27x

=> 9x + 18 = 27x

=> 9x + 18 - 27x = 0

=> 9x - 27x + 18 = 0

=> -18x = -18

=> x = 1

b/ \(\frac{-7}{x}=\frac{21}{34-x}\)

=> -7(34 - x) = 21x

=>  -238 + 7x = 21x

=> 21x - 7x = -238

=> -14x = 238

=> x = -17

c) \(\frac{-8}{15}< \frac{x}{40}< \frac{-7}{15}\)

Ta có BCNN(15,40,15) = 120

=> \(\frac{-64}{120}< \frac{3x}{120}< \frac{-56}{120}\)

=> -64 < 3x < -56

=> x \(\in\){ -19;-20;-21}

Câu d tương tự

d) \(\frac{-1}{2}< \frac{x}{18}< \frac{-1}{3}\)

\(\Leftrightarrow\frac{-9}{18}< \frac{x}{18}< \frac{-6}{18}\)

\(\Leftrightarrow-9< x< -6\)

\(\Rightarrow x\in\left\{-8;-7\right\}\)

a) \(\left(6\frac{2}{7}x+\frac{3}{7}\right)\cdot\frac{11}{5}-\frac{3}{7}=-2\)

=> \(\left(\frac{44}{7}x+\frac{3}{7}\right)\cdot\frac{11}{5}=-\frac{11}{7}\)

=> \(\frac{44}{7}x+\frac{3}{7}=-\frac{5}{7}\)

=> \(\frac{44}{7}x=-\frac{8}{7}\)

=> \(\frac{44x}{7}=-\frac{8}{7}\)

=> 44x = -8 => 11x = -2 => \(x=-\frac{2}{11}\)

b) \(3\frac{1}{4}x+\left(-\frac{7}{6}\right)-1\frac{2}{3}=\frac{5}{12}\)

=> \(\frac{13}{4}x-\frac{7}{6}-1\frac{2}{3}=\frac{5}{12}\)

=> \(\frac{13}{4}x-\frac{7}{6}=\frac{25}{12}\)

=> \(\frac{13}{4}x=\frac{13}{4}\)

=> x = 1

c) \(\left(x+\frac{1}{2}\right)\left(\frac{2}{3}-2x\right)=0\)

=> \(\orbr{\begin{cases}x+\frac{1}{2}=0\\\frac{2}{3}-2x=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-\frac{1}{2}\\x=\frac{1}{3}\end{cases}}\)

d) \(\left(x+\frac{1}{5}\right)^2+\frac{17}{25}=\frac{26}{25}\)

=> \(\left(x+\frac{1}{5}\right)^2=\frac{9}{25}=\left(\frac{3}{5}\right)^2\)

=> \(\orbr{\begin{cases}x+\frac{1}{5}=\frac{3}{5}\\x+\frac{1}{5}=-\frac{3}{5}\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{2}{5}\\x=-\frac{4}{5}\end{cases}}\)

e) \(-1\frac{5}{27}-\left(3x-\frac{7}{9}\right)^3=\frac{-24}{27}\)

=> \(\left(3x-\frac{7}{9}\right)^3=-1\frac{5}{27}-\left(-\frac{24}{27}\right)=-\frac{32}{27}+\frac{24}{27}=-\frac{8}{27}\)

=> \(\left(3x-\frac{7}{9}\right)^3=\left(-\frac{2}{3}\right)^3\)

=> \(3x-\frac{7}{9}=-\frac{2}{3}\)

=> \(x=\frac{-\frac{2}{3}+\frac{7}{9}}{3}=\frac{1}{27}\)

g) \(\frac{x}{1\cdot2}+\frac{x}{2\cdot3}+\frac{x}{3\cdot4}+...+\frac{x}{99\cdot100}=\frac{99}{100}\)

=> \(\frac{x}{1}-\frac{x}{2}+\frac{x}{2}-\frac{x}{3}+...+\frac{x}{99}-\frac{x}{100}=\frac{99}{100}\)

=> \(\frac{x}{1}-\frac{x}{100}=\frac{99}{100}\)

=> \(\frac{100x-x}{100}=\frac{99}{100}\)

=> \(\frac{99x}{100}=\frac{99}{100}\)

=> x = 1

h) \(\frac{x}{3}+\frac{x}{6}+\frac{x}{10}+\frac{x}{15}=3x-1\)

=> \(\frac{2x}{6}+\frac{2x}{12}+\frac{2x}{20}+\frac{2x}{30}=3x-1\)

=> \(\frac{2x}{2\cdot3}+\frac{2x}{3\cdot4}+\frac{2x}{4\cdot5}+\frac{2x}{5\cdot6}=3x-1\)

=> \(2\left(\frac{x}{2\cdot3}+\frac{x}{3\cdot4}+\frac{x}{4\cdot5}+\frac{x}{5\cdot6}\right)=3x-1\)

=> \(2\left(\frac{x}{2}-\frac{x}{6}\right)=3x-1\)

=> \(2\left(\frac{3x}{6}-\frac{x}{6}\right)=3x-1\)

=> \(2\cdot\frac{2x}{6}=3x-1\)

=> \(\frac{x}{3}=\frac{3x-1}{2}\)

=> 2x = 3(3x - 1)

=> 2x - 9x + 3  = 0

=> -7x = -3

=> x = 3/7

a)\(\left(4\frac{5}{37}-3\frac45+8\frac{15}{29}\right)-\left(3\frac{5}{57}-6\frac{14}{29}\right)\)

=\(4\frac{5}{37}-3\frac45+8\frac{15}{29}-3\frac{5}{37}+6\frac{14}{29}\)

=\(\left(4\frac{5}{37}-3\frac{5}{37}\right)+\left(8\frac{15}{29}+6\frac{14}{29}\right)-3\frac45\)

=\(\left\lbrack\left(4-3\right)+\left(\frac{5}{37}-\frac{5}{37}\right)\right\rbrack+\left\lbrack\left(8+6\right)+\left(\frac{15}{29}\right.\right.\)+\(\frac{14}{29})\) -\(\frac{19}{5}\)

=\(1+0+14+1-\frac{19}{5}\)

=\(15+1-\frac{19}{5}\)

=\(16-\frac{19}{5}\)

=\(\frac{80}{5}-\frac{19}{5}\)

=\(\frac{61}{5}\)