1/2x + 1/5 = 2/3x - 1/4

=> 1/2x - 2/3x = -1/4 - 1/5

=> -1/6x = -9/20

=> x = -9/20 : (-1/6)

=> x = 27/10

\(\frac{1}{2}x+\frac{1}{5}=\frac{2}{3}x-\frac{1}{4}\)

\(\frac{1}{2}x=\frac{2}{3}x-\frac{1}{4}-\frac{1}{5}\)

\(\frac{1}{2}x=-\frac{9}{20}+\frac{2x}{3}\)

\(\frac{1}{2}x=-\frac{9}{20}+\frac{2x}{3}-\frac{2x}{3}\)

\(-\frac{x}{6}=-\frac{9}{20}\)

\(6\left(-\frac{x}{6}\right)=6\left(-\frac{9}{20}\right)\)

\(-x=-\frac{27}{10}\)

\(\Rightarrow x=-\frac{27}{10}\)

1)

\((x+2)(x+3)(x+4)(x+5)-24\\=[(x+2)(x+5)]\cdot[(x+3)(x+4)]-24\\=(x^2+7x+10)(x^2+7x+12)-24\)

Đặt \(x^2+7x+10=y\), khi đó biểu thức trở thành:

\(y(y+2)-24\\=y^2+2y-24\\=y^2+2y+1-25\\=(y+1)^2-5^2\\=(y+1-5)(y+1+5)\\=(y-4)(y+6)\\=(x^2+7x+10-4)(x^2+7x+10+6)\\=(x^2+7x+6)(x^2+7x+16)\)

2) Bạn xem lại đề!

3/7 + 1/2 - 17/7 +3/2

=(1/2+3/2) + (3/7-17/7)

=2+-2

=0

2/9 x 4 + 1/3 = 8/9 + 1/3 = 8/9 + 3/9 = 11/9

8/9+1/3

11/9

\(=\dfrac{11}{9}\)

a) \(\dfrac{1}{2}-\left(x+\dfrac{1}{3}\right)=\dfrac{5}{6}\)

\(\Rightarrow x+\dfrac{1}{3}=\dfrac{1}{2}-\dfrac{5}{6}\)

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

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

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

b)\(\dfrac{3}{4}-\left(x+\dfrac{1}{2}\right)=\dfrac{4}{5}\)

\(\Rightarrow x+\dfrac{1}{2}=\dfrac{3}{4}-\dfrac{4}{5}\)

\(\Rightarrow x+\dfrac{1}{2}=\dfrac{-1}{20}\)

\(\Rightarrow x=\dfrac{-1}{20}-\dfrac{1}{2}\)

\(\Rightarrow x=\dfrac{-11}{20}\)

c) \(\dfrac{3}{35}-\left(\dfrac{3}{5}+x\right)=\dfrac{2}{7}\)

\(\Rightarrow\dfrac{3}{5}+x=\dfrac{3}{35}-\dfrac{2}{7}\)

\(\Rightarrow\dfrac{3}{5}+x=\dfrac{-1}{5}\)

\(\Rightarrow x=\dfrac{-1}{5}-\dfrac{3}{5}\)

\(\Rightarrow x=\dfrac{-4}{5}\)

d)\(\dfrac{2}{3}.x=\dfrac{4}{27}\)

\(\Rightarrow x=\dfrac{4}{27}:\dfrac{2}{3}\)

\(\Rightarrow x=\dfrac{2}{9}\)

e) \(\dfrac{-3}{5}.x=\dfrac{21}{10}\)

\(\Rightarrow x=\dfrac{21}{10}:\dfrac{-3}{5}\)

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

\(\left(\frac{x}{2}-\frac{1}{3}\right):\frac{1}{2}=\left(\frac{1}{4}-\frac{3}{2}\right):\left(1-\frac{5}{4}\right)\)

\(\left(\frac{3x-2}{6}\right):\frac{1}{2}=\left(-\frac{5}{4}\right):\left(-\frac{1}{4}\right)\)

\(\left(\frac{3x-2}{6}\right):\frac{1}{2}=5\)

\(\left(\frac{3x-2}{6}\right)=\frac{5}{2}\)

           Áp dụng công thức \(\frac{a}{b}=\frac{c}{d}\Rightarrow ad=bc\) ta đc:

                    \(\Rightarrow2\left(3x-2\right)=30\)

                    \(\Rightarrow\left(3x-2\right)=15\)

                    \(\Rightarrow3x=17\)

                         \(\Rightarrow x=\frac{17}{3}\)

\(\left(\frac{x}{2}-\frac{1}{3}\right):\frac{1}{2}=\left(\frac{1}{4}-\frac{3}{2}\right):\left(\frac{1-5}{4}\right)\)

\(\left(\frac{x}{2}-\frac{1}{3}\right):\frac{1}{2}=\left(\frac{1}{4}-\frac{6}{4}\right):1\)

\(\left(\frac{x}{2}-\frac{1}{3}\right):\frac{1}{2}=-\frac{5}{4}:1\)

\(\left(\frac{x}{2}-\frac{1}{3}\right):\frac{1}{2}=-\frac{5}{4}\)

\(\frac{x}{2}-\frac{1}{3}=-\frac{5}{4}\times\frac{1}{2}\)

\(\frac{x}{2}-\frac{1}{3}=-\frac{5}{8}\)

\(\frac{x}{2}=-\frac{5}{8}+\frac{1}{3}\)

\(\frac{x}{2}=-\frac{7}{24}\)

\(x\times24=-14\)

\(x=-\frac{7}{12}\)

Hình như có gì đó sai sai Chị ah

3|x-1|+2|x-4|=x+17

x=-1,

x=7

nha bạn chúc bạn học tốt nha 

yes yes yes

mọi người có thể giải cụ thể được không ạ