\(\frac{x+2015}{5}+\frac{x+2016}{4}=\frac{x+2017}{3}+\frac{x+2018}{2}\)

\(\Leftrightarrow\left(\frac{x+2015}{5}+1\right)+\left(\frac{x+2016}{4}+1\right)=\left(\frac{x+2017}{3}+1\right)+\left(\frac{x+2018}{2}+1\right)\)

\(\Leftrightarrow\frac{x+2020}{5}+\frac{x+2020}{4}-\frac{x+2020}{3}-\frac{x+2020}{2}=0\)

\(\Leftrightarrow\left(x+2020\right)\left(\frac{1}{5}+\frac{1}{4}-\frac{1}{3}-\frac{1}{2}\right)=0\)

\(\Leftrightarrow x+2020=0\)vì \(\frac{1}{5}+\frac{1}{4}+\frac{1}{3}+\frac{1}{2}\ne0\)

\(\Leftrightarrow x=-2020\)

khó lắm

bây h thì bạn giải đc chưa

Cảm ơn bạn rất nhiều mình đã hiểu rồi 

Chúc bạn học tốt nhé

\(\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1+0.\)

\(=\left(\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x\right)+1\)

\(=x\left(\frac{1}{6}+\frac{1}{10}-\frac{4}{15}\right)+1\)

\(=x\left(\frac{1\cdot5}{30}+\frac{1\cdot3}{30}-\frac{4\cdot2}{30}\right)+1\)

\(=x\left(\frac{5}{30}+\frac{3}{30}-\frac{8}{30}\right)+1\)

\(=x\left(\frac{5+3-8}{30}\right)+1\)

\(=x\cdot0+1=1\)

\(\Rightarrow\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1+0=1\)

trả lời:

  \frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1+0.61​x+101​x−154​x+1+0.

=\left(\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x\right)+1=(61​x+101​x−154​x)+1

=x\left(\frac{1}{6}+\frac{1}{10}-\frac{4}{15}\right)+1=x(61​+101​−154​)+1

=x\left(\frac{1\cdot5}{30}+\frac{1\cdot3}{30}-\frac{4\cdot2}{30}\right)+1=x(301⋅5​+301⋅3​−304⋅2​)+1

=x\left(\frac{5}{30}+\frac{3}{30}-\frac{8}{30}\right)+1=x(305​+303​−308​)+1

=x\left(\frac{5+3-8}{30}\right)+1=x(305+3−8​)+1

=x\cdot0+1=1=x⋅0+1=1

\Rightarrow\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1+0=1⇒61​x+101​x−154​x+1+0=1

ko chắc chúc bạn học tốt.

\(\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1=0\)

\(\frac{5}{30}x+\frac{3}{30}x-\frac{8}{30}x+1=0\)

\(\frac{8}{30}x-\frac{8}{30}x+1=0\)

\(0+1=0\)

\(\text{Mình thấy bài này có gì sai sai sai thì phải bạn à !}\)

xin lỗi các bạn nhé =1 chứ không phải =0                                                                                                                                           thông cảm cho mik nhé^^^

Bài làm

\(\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1=0\)

\(x\left(\frac{1}{6}+\frac{1}{10}-\frac{4}{15}\right)+1=0\)

\(x\left(\frac{5}{30}+\frac{3}{30}-\frac{8}{30}\right)+1=40\)

\(x.\frac{1}{30}+1=0\)

\(x\frac{1}{3}=-1\)

\(x=-1:\frac{1}{3}\)

\(x=-1.3\)

\(x=-3\)

# Học tốt #

\(\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x\left(x-1\right)}=\frac{2007}{2009}\)

\(2\cdot\left(\frac{1}{6}+\frac{1}{12}+..+\frac{1}{x\left(x-1\right)}\right)=\frac{2007}{2009}\)

\(\frac{1}{6}+\frac{1}{12}+..+\frac{1}{x\left(x-1\right)}=\frac{2007}{2009}:2\)

\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{\left(x-1\right)x}=\frac{2007}{4018}\)

\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{x-1}-\frac{1}{x}=\frac{2007}{4018}\)

\(\frac{1}{2}-\frac{1}{x}=\frac{2007}{4018}\)

\(\frac{1}{x}=\frac{1}{2}-\frac{2007}{4018}\)

\(\frac{1}{x}=\frac{1}{2009}\)

=> x = 2009 

\(a,\left(\frac{1}{7}x-\frac{2}{7}\right)\left(-\frac{1}{5}x+\frac{3}{5}\right)\left(\frac{1}{3}x+\frac{4}{3}\right)=0\)

TH1 : \(\frac{1}{7}x-\frac{2}{7}=0\Rightarrow\frac{x-2}{7}=0\Rightarrow x-2=0\Leftrightarrow x=2\)

TH2 : \(-\frac{1}{5}x+\frac{3}{5}=0\Rightarrow\frac{-x+3}{5}=0\Rightarrow-x+3=0\Leftrightarrow x=3\)

TH3 : \(\frac{1}{3}x+\frac{4}{3}=0\Rightarrow\frac{x+4}{3}=0\Rightarrow x+4=0\Leftrightarrow x=-4\)

\(\Rightarrow x\in\left\{2;3;-4\right\}\)

\(b,\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1=0\)

\(\Rightarrow\frac{5}{30}x+\frac{3}{30}x-\frac{8}{30}x+1=0\)

\(\Rightarrow\frac{5x+3x-8x}{30}+1=0\)

\(\Rightarrow1=0\)( vô lý )\(\Rightarrow x\in\varnothing\)

a) (1/7x - 2/7)(-1/5x + 3/5)(1/3x + 4/3) = 0

3 trường hợp:

TH1: 1/7x - 2/7 = 0 <=> 1/7x = 0 + 2/7 <=> 1/7x = 2/7 <=> x = 2.7/7 = 2

=> x = 2

TH2: -1/5x + 3/5 = 0 <=> -1/5x = 0 - 3/5 <=> -1/5x = -3/5 <=> x = (-3/5).(-5) = 3

=> x = 3

TH3: 1/3x + 4/3 = 0 <=> 1/3x = 0 - 4/3 <=> 1/3x = -4/3 <=> x = x = 3.(-4/3) = -4

=> x = -4

Vậy: x = 2, 3, -4

b) 1/6x + 1/10x - 4/15x + 1 = 0

<=> 1/6x + 1/10x - 4/15x = 0 - 1

<=> 1/6x + 1/10x - 4/15x = -1

<=> 1/6x.30 + 1/10x.30 - 4/15x.30 = -1.30

<=> 5x + 3x - 8x = -30

<=> 0 = -30

=> không có x thỏa mãn

a, \(\frac{1}{6}x+\frac{1}{10}-\frac{4}{15}x+1=0\)

\(\Leftrightarrow-\frac{1}{10}x=-\frac{11}{10}\)

\(\Leftrightarrow x=11\)

b,\(\left(\frac{1}{7}x-\frac{2}{7}\right)\left(-\frac{1}{5}x+\frac{3}{5}\right)\left(\frac{1}{3}x+\frac{4}{3}\right)=0\)

\(\Leftrightarrow\frac{1}{7}x-\frac{2}{7}=0\)hoặc \(-\frac{1}{5}x+\frac{3}{5}=0\)hoặc \(\frac{1}{3}x+\frac{4}{3}=0\)

+) \(\frac{1}{7}x-\frac{2}{7}=0\Leftrightarrow\frac{1}{7}x=\frac{2}{7}\Leftrightarrow x=2\)

+)\(-\frac{1}{5}x+\frac{3}{5}=0\Leftrightarrow-\frac{1}{5}x=-\frac{3}{5}\Leftrightarrow x=3\)

+)\(\frac{1}{3}x+\frac{4}{3}=0\Leftrightarrow\frac{1}{3}x=-\frac{4}{3}\Leftrightarrow x=-4\)

  c, \(\frac{1}{2}x-\frac{11}{15}:\frac{33}{35}=-\frac{1}{3}\)

\(\Leftrightarrow\frac{1}{2}x-\frac{7}{9}=-\frac{1}{3}\)

\(\Leftrightarrow\frac{1}{2}x=\frac{4}{9}\)

\(\Leftrightarrow x=\frac{8}{9}\)

a/ \(\frac{1}{6}x+\frac{1}{10}-\frac{4}{15}x+1=0\)

    \(\Rightarrow-\frac{1}{10}x=-\frac{11}{10}\)

     \(\Rightarrow x=11\)

b/ \(\left(\frac{1}{7}x-\frac{2}{7}\right)\left(-\frac{1}{5}x+\frac{3}{5}\right)\left(\frac{1}{3}x+\frac{4}{3}\right)=0\)

   \(\Rightarrow\frac{1}{7}x-\frac{2}{7}=0\Rightarrow\frac{1}{7}x=\frac{2}{7}\Rightarrow x=2\)

hoặc \(-\frac{1}{5}x+\frac{3}{5}=0\Rightarrow-\frac{1}{5}x=-\frac{3}{5}\Rightarrow x=3\)

hoặc \(\frac{1}{3}x+\frac{4}{3}=0\Rightarrow\frac{1}{3}x=-\frac{4}{3}\Rightarrow x=-4\)

                                              Vậy x = 2, x = 3, x = -4

c/ \(\frac{1}{2}x-\frac{11}{15}:\frac{33}{35}=-\frac{1}{3}\)

     \(\Rightarrow\frac{1}{2}x-\frac{7}{9}=-\frac{1}{3}\)

      \(\Rightarrow\frac{1}{2}x=\frac{4}{9}\Rightarrow x=\frac{8}{9}\)

                                                                       Vậy x = 8/9

Ta có : \(\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1=0\)

<=> \(\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x=-1\)

<=> \(\left(\frac{1}{6}+\frac{1}{10}-\frac{4}{15}\right)x=-1\)

<=> \(0.x=-1\)

=> x thuộc rỗng 

\(\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1=0\)

\(\Leftrightarrow\left(\frac{1}{6}+\frac{1}{10}-\frac{4}{15}\right)x+1=0\)

\(\Leftrightarrow\left(\frac{5}{30}+\frac{3}{30}-\frac{8}{30}\right)x+1=0\)

\(\Leftrightarrow\frac{5+3-8}{30}x+1=0\)

\(\Leftrightarrow0x=-1\)(vô lí)

vậy không có giá trị nào của x thỏa mãn. 

b, \(x\left(\frac{1}{6}+\frac{1}{10}-\frac{4}{15}\right)+1=0\)

        \(0+1=0\)

=> x thuoc rong