2: =>2x-1/4=5/6-1/2x

=>5/2x=5/6+1/4=13/12

=>x=13/30

3: =>3x-5/6=2/3-1/2x

=>3,5x=2/3+5/6=4/6+5/6=9/6=3,2

hay x=32/35

a) Đặt \(x-1=a\)

\(pt\Leftrightarrow\frac{13}{a}+\frac{5}{2a}=\frac{6}{3a}\)

\(\Leftrightarrow\frac{31}{2a}=\frac{6}{3a}\)

\(\Leftrightarrow\frac{31}{2}=2\)(vô lí)

Vậy pt vô nghiệm

a) \(\frac{13}{x-1}+\frac{5}{2x-2}=\frac{6}{3x-3}\)

\(\frac{13}{x-1}+\frac{5}{2\left(x-1\right)}=\frac{6}{3\left(x-1\right)}\)

\(\frac{13}{x-1}+\frac{5}{2\left(x-1\right)}=\frac{2}{x-1}\)

\(\frac{31}{2\left(x-1\right)}=\frac{2}{x-1}\)

\(\frac{31}{2}=2\)

=> không có x thỏa mãn đề bài.

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

\(\frac{1}{x-1}+\frac{-2}{3}.\frac{-9}{20}=\frac{5}{2\left(1-x\right)}\)

\(\frac{1}{x-1}-\frac{-18}{60}=\frac{5}{2\left(1-x\right)}\)

\(\frac{1}{x-1}+\frac{3}{10}=\frac{5}{2\left(1-x\right)}\)

\(10\left(1-x\right)+3\left(x-1\right)\left(1-x\right)=25\left(x-1\right)\)

\(7-4x-3x^2=25x-25\)

\(7-4x-3x^2-25x+25=0\)

\(32-29x-3x^2=0\)

\(3x^2+29x-30=0\)

\(3x^2+32x-3x-32=0\)

\(x\left(3x+32\right)-\left(3x+32\right)=0\)

\(\left(3x+32\right)\left(x-1\right)=0\)

\(\orbr{\begin{cases}3x+32=0\\x-1=0\end{cases}}\)

\(\orbr{\begin{cases}x=-\frac{32}{3}\\x=1\end{cases}}\)

Đăng từng bài thôi chứ bạn

mất công lém

a, \(-\frac{5}{7}-\left(\frac{1}{2}-x\right)=-\frac{11}{4}\)

\(\frac{1}{2}-x=\frac{57}{28}\)

\(x=-\frac{43}{28}\)

b, \(\left(2x-1\right)^2-5=20\)

\(\Rightarrow\left(2x-1\right)^2=25\)

\(\Rightarrow2x-1=\pm5\)

\(\Rightarrow\left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=6\\2x=-4\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)

Câd

\(\frac{x-6}{4}=\frac{4}{x-6}\)

(\(x-6\))(\(x-6\)) =4.4

(\(x-6\))\(^2\) = 4\(^2\)

\(x-6=-4\) hoặc \(x\) - 6 = 4

\(x-6\) = -4

\(x=-4+6\)

\(x=2\)

\(x-6=4\)

\(x=4+6\)

\(x=10\)

Vậy \(x\) ∈ {2; 10}

b, \(\left(2x-1\right)^2-5=20\)

\(\Rightarrow\left(2x-1\right)^2=25\)

\(\Rightarrow\left(2x-1\right)^2=5^2\)

\(\Rightarrow\left[{}\begin{matrix}2x-1=6\\2x-1=-6\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=7\\2x=-5\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\frac{7}{2}\\x=-\frac{5}{2}\end{matrix}\right.\)

Vậy ...

a) \(-\frac{5}{7}-\left(\frac{1}{2}-x\right)=\frac{-11}{4}\)

\(\Rightarrow\left(\frac{1}{2}-x\right)=\left(-\frac{5}{7}\right)+\frac{11}{4}\)

\(\Rightarrow\frac{1}{2}-x=\frac{57}{28}\)

\(\Rightarrow x=\frac{1}{2}-\frac{57}{28}\)

\(\Rightarrow x=-\frac{43}{28}\)

Vậy \(x=-\frac{43}{28}.\)

b) \(\left(2x-1\right)^2-5=20\)

\(\Rightarrow\left(2x-1\right)^2=20+5\)

\(\Rightarrow\left(2x-1\right)^2=25\)

\(\Rightarrow2x-1=\pm5\)

\(\Rightarrow\left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=5+1=6\\2x=\left(-5\right)+1=-4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=6:2\\x=\left(-4\right):2\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)

Vậy \(x\in\left\{3;-2\right\}.\)

d) \(\frac{x-6}{4}=\frac{4}{x-6}\)

\(\Rightarrow\left(x-6\right).\left(x-6\right)=4.4\)

\(\Rightarrow\left(x-6\right).\left(x-6\right)=16\)

\(\Rightarrow\left(x-6\right)^2=16\)

\(\Rightarrow x-6=\pm4\)

\(\Rightarrow\left[{}\begin{matrix}x-6=4\\x-6=-4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4+6\\x=\left(-4\right)+6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=10\\x=2\end{matrix}\right.\)

Vậy \(x\in\left\{10;2\right\}.\)

Chúc bạn học tốt!

#)Giải :

a) x + 2x + 3x + ... + 100x = - 213

=> 100x + ( 2 + 3 + 4 + ... + 100 ) = - 213 

=> 100x + 5049 = - 213 

<=> 100x = - 5262

<=> x = - 52,62

#)Giải :

b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}x-\frac{1}{6}\)

\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{3}+\frac{1}{6}\)

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

\(\Rightarrow\left(\frac{1}{2}+\frac{1}{4}\right)x=\frac{1}{2}\)

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

\(\Leftrightarrow x=\frac{2}{3}\)