`@` `\text {Ans}`

`\downarrow`

`1/2*x + 3/5*(x - 2) = 3`

`=> 1/2*x + 3/5*x - 3/5*2 = 3`

`=> 1/2x + 3/5x - 6/5 = 3`

`=> (1/2 + 3/5)x - 6/5 = 3`

`=> 11/10x - 6/5 = 3`

`=> 11/10x = 3 + 6/5`

`=> 11/10x =21/5`

`=> x = 21/5 \div 11/10`

`=> x = 42/11`

Vậy, `x = 42/11`

____

`3 - (1/6 - x)*2/3 = 2/3`

`=> (1/6 - x)*2/3 = 3 - 2/3`

`=> (1/6 - x)*2/3 = 7/3`

`=> 1/6 - x = 7/3 \div 2/3`

`=> 1/6 - x=7/2`

`=> x = 1/6 - 7/2`

`=> x = -10/3`

Vậy, `x = -10/3.`

\(\dfrac{1}{2}\cdot x+\dfrac{3}{5}\left(x-2\right)=3\\ \dfrac{1}{2}\cdot x+\dfrac{3}{5}\cdot x-\dfrac{13}{5}=3\\ \left(\dfrac{1}{2}+\dfrac{3}{5}\right)x-\dfrac{13}{5}=3\\ \dfrac{11}{10}x-\dfrac{13}{5}=3\\ \dfrac{11}{10}x=\dfrac{28}{5}\\ x=\dfrac{28}{5}:\dfrac{11}{10}\\ x=\dfrac{28}{11}\\ 3-\left(\dfrac{1}{6}-x\right)\cdot\dfrac{2}{3}=\dfrac{2}{3}\\ \left(\dfrac{1}{6}-x\right)\cdot\dfrac{2}{3}=3-\dfrac{2}{3}\\ \left(\dfrac{1}{6}-x\right)\cdot\dfrac{2}{3}=\dfrac{7}{3}\\ \dfrac{1}{6}-x=\dfrac{7}{3}:\dfrac{2}{3}\\ \dfrac{1}{6}-x=\dfrac{7}{2}\\ x=\dfrac{1}{6}-\dfrac{7}{2}\\ x=-\dfrac{10}{3}\)

x= 4211

\(x+\dfrac{1}{2}=\dfrac{33}{4}\\ \Rightarrow x=\dfrac{33}{4}-\dfrac{1}{2}\\ \Rightarrow x=\dfrac{31}{4}\\ \dfrac{5}{6}-x=\dfrac{1}{3}\\ \Rightarrow x=\dfrac{5}{6}-\dfrac{1}{3}\\ \Rightarrow x=\dfrac{1}{2}\\ x+\dfrac{4}{5}=\dfrac{-2}{3}\\ \Rightarrow x=\dfrac{-2}{3}-\dfrac{4}{5}\\ \Rightarrow x=\dfrac{-22}{15}\)

\(\Leftrightarrow\left(11+\dfrac{7}{18}-9-\dfrac{13}{18}\right):x=\dfrac{5}{3}+\dfrac{35}{33}\cdot\dfrac{11}{7}=\dfrac{10}{3}\)

\(\Leftrightarrow x=\dfrac{5}{3}:\dfrac{10}{3}=\dfrac{1}{2}\)

\(\left(x+\dfrac{2}{3}\right)+\dfrac{1}{11}=\left(\dfrac{10}{-33}.\dfrac{11}{8}\right).\dfrac{24}{-55}\)

\(\Rightarrow\left(x+\dfrac{2}{3}\right)+\dfrac{1}{11}=\dfrac{-5}{12}.\dfrac{24}{-55}\)

\(\Rightarrow\left(x+\dfrac{2}{3}\right)+\dfrac{1}{11}=\dfrac{2}{11}\)

\(\Rightarrow x+\dfrac{2}{3}=\dfrac{2}{11}-\dfrac{1}{11}\)

\(\Rightarrow x+\dfrac{2}{3}=\dfrac{1}{11}\)

\(\Rightarrow x=\dfrac{1}{11}-\dfrac{2}{3}\)

\(\Rightarrow x=-\dfrac{19}{33}\)

(x + 2/3) + 1/11 = [10/(-33) . 11/8] . 24/(-55)

(x + 2/3) + 1/11 = -5/12 . 24/(-55)

(x + 2/3) + 1/11 = 2/11

x + 2/3 = 2/11 - 1/11

x + 2/3 = 1/11

x = 1/11 - 2/3

x = -19/33

1: Ta có: \(\dfrac{x}{3}=\dfrac{y}{6}\)

mà 4x-y=42

nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{3}=\dfrac{y}{6}=\dfrac{4x-y}{4\cdot3-6}=\dfrac{42}{12-6}=\dfrac{42}{6}=7\)

=>\(x=7\cdot3=21;y=6\cdot7=42\)

2: \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}\)

mà x-2y+3z=33

nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}=\dfrac{x-2y+3z}{2-2\cdot3+3\cdot5}=\dfrac{33}{2-6+15}=\dfrac{33}{11}=3\)

=>\(x=3\cdot2=6;y=3\cdot3=9;z=3\cdot5=15\)

3: \(\dfrac{x}{y}=\dfrac{6}{5}\)

=>\(\dfrac{x}{6}=\dfrac{y}{5}\)

mà x+y=121

nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{6}=\dfrac{y}{5}=\dfrac{x+y}{6+5}=\dfrac{121}{11}=11\)

=>\(x=11\cdot6=66;y=11\cdot5=55\)

\(\dfrac{9}{5}+\dfrac{5}{7}+\dfrac{7}{5}+\dfrac{3}{7}=\left(\dfrac{9}{5}+\dfrac{7}{5}\right)+\left(\dfrac{5}{7}+\dfrac{3}{7}\right)=\dfrac{16}{5}+\dfrac{8}{7}=\dfrac{112}{35}+\dfrac{40}{35}=\dfrac{152}{35}\)

\(\dfrac{1}{2}\times\dfrac{45}{33}\times\dfrac{1}{9}\times\dfrac{11}{6}=\dfrac{1}{2}\times\dfrac{15}{11}\times\dfrac{1}{9}\times\dfrac{11}{6}=\left(\dfrac{1}{2}\times\dfrac{1}{9}\right)\times\left(\dfrac{15}{11}\times\dfrac{11}{6}\right)=\dfrac{1}{18}\times\dfrac{15}{6}=\dfrac{5}{36}\)

\(\left(\dfrac{103}{8}-\dfrac{193}{18}\right):x-\dfrac{40}{33}:\dfrac{8}{11}=\dfrac{5}{3}\)

\(\dfrac{155}{72}:x-\dfrac{5}{3}=\dfrac{5}{3}\)

\(\dfrac{155}{72}:x=\dfrac{5}{3}+\dfrac{5}{3}=\dfrac{10}{3}\)

\(x=\dfrac{155}{72}:\dfrac{10}{3}=\dfrac{31}{48}\)

vaayj.....

5/3:x-5/3=5/3

5/3:x=5/3+5/3

5/3:x=10/3

x=5/3:10/3

x=1/2

1) PT \(\Leftrightarrow\left(\dfrac{x+1}{35}+1\right)+\left(\dfrac{x+3}{33}+1\right)=\left(\dfrac{x+5}{31}+1\right)+\left(\dfrac{x+7}{29}+1\right)\)

\(\Leftrightarrow\dfrac{x+36}{35}+\dfrac{x+36}{33}=\dfrac{x+36}{31}+\dfrac{x+36}{29}\)

\(\Leftrightarrow\left(x+36\right)\left(\dfrac{1}{29}+\dfrac{1}{31}-\dfrac{1}{33}-\dfrac{1}{35}\right)=0\)

\(\Leftrightarrow x+36=0\) (Do \(\dfrac{1}{29}+\dfrac{1}{31}-\dfrac{1}{33}-\dfrac{1}{35}>0\))

\(\Leftrightarrow x=-36\).

Vậy nghiệm của pt là x = -36.

2) x(x+1)(x+2)(x+3)= 24

⇔ x.(x+3)  .   (x+2).(x+1)  = 24

⇔(\(x^2\) + 3x) . (\(x^2\) + 3x + 2) = 24

Đặt \(x^2\)+ 3x = b

⇒ b . (b+2)= 24

Hay: \(b^2\) +2b = 24

⇔\(b^2\) + 2b + 1 = 25

⇔\(\left(b+1\right)^2\)= 25

+ Xét b+1 = 5 ⇒ b=4 ⇒  \(x^2\)+ 3x = 4 ⇒ \(x^2\)+4x-x-4=0 ⇒x(x+4)-(x+4)=0

⇒(x-1)(x+4)=0⇒x=1 và x=-4

+ Xét b+1 = -5 ⇒ b=-6 ⇒ \(x^2\)+3x=-6 ⇒\(x^2\) + 3x + 6=0

⇒\(x^2\) + 2.x.\(\dfrac{3}{2}\) + (\(\dfrac{3}{2}\))² = - \(\dfrac{15}{4}\)  Hay ( \(x^2\) +\(\dfrac{3}{2}\) )²= -\(\dfrac{15}{4}\) (vô lí)

⇒x= 1 và x= 4

\(=\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times...\times\dfrac{2021}{2022}\\ \dfrac{1}{2022}\)

a. \(\dfrac{1}{2}x+\dfrac{3}{5}x=\dfrac{-33}{25}\)

\(\Rightarrow\dfrac{11}{10}x=\dfrac{-33}{25}\)

\(\Rightarrow x=\dfrac{-33}{25}:\dfrac{11}{10}=\dfrac{-6}{5}\)

Vậy.........

b. \(\left(\dfrac{2}{3}x-\dfrac{4}{9}\right)\left(\dfrac{1}{2}+\dfrac{-3}{7}:x\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}\dfrac{2}{3}x-\dfrac{4}{9}=0\\\dfrac{1}{2}+\dfrac{-3}{7}:x=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\dfrac{2}{3}x=\dfrac{4}{9}\\\dfrac{-3}{7}:x=\dfrac{-1}{2}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=\dfrac{6}{7}\end{matrix}\right.\)

Vậy................

a, 1/2xX+3/5xX=-33/25

Xx(1/2+3/5)=-33/25

Xx11/10=-33/25

X=-6/5

b,