1a) \(\left|\frac{3}{2}x+\frac{1}{2}\right|=\left|4x-1\right|\)

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

=> \(\orbr{\begin{cases}-\frac{5}{2}x=-\frac{3}{2}\\\frac{11}{2}x=\frac{1}{2}\end{cases}}\)

=> \(\orbr{\begin{cases}x=\frac{5}{3}\\x=\frac{1}{11}\end{cases}}\)

b) \(\left|\frac{5}{4}x-\frac{7}{2}\right|-\left|\frac{5}{8}x+\frac{3}{5}\right|=0\)

=>\(\left|\frac{5}{4}x-\frac{7}{2}\right|=\left|\frac{5}{8}x+\frac{3}{5}\right|\)

=> \(\orbr{\begin{cases}\frac{5}{4}x-\frac{7}{2}=\frac{5}{8}x+\frac{3}{5}\\\frac{5}{4}x-\frac{7}{2}=-\frac{5}{8}x-\frac{3}{5}\end{cases}}\)

=> \(\orbr{\begin{cases}\frac{5}{8}x=\frac{41}{10}\\\frac{15}{8}x=\frac{29}{10}\end{cases}}\)

=> \(\orbr{\begin{cases}x=\frac{164}{25}\\x=\frac{116}{75}\end{cases}}\)

c) TT

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

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

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

=> \(\orbr{\begin{cases}x=\frac{3}{5}\\x=\frac{1}{11}\end{cases}}\)

\(b,\left|\frac{5}{4}x-\frac{7}{2}\right|-\left|\frac{5}{8}x+\frac{3}{5}\right|=0\)

=> \(\left|\frac{5}{4}x-\frac{7}{2}\right|-0=\left|\frac{5}{8}x+\frac{3}{5}\right|\)

=> \(\frac{\left|5x-14\right|}{4}=\frac{\left|25x+24\right|}{40}\)

=> \(\frac{10(\left|5x-14\right|)}{40}=\frac{\left|25x+24\right|}{40}\)

=> \(\left|50x-140\right|=\left|25x+24\right|\)

=> \(\orbr{\begin{cases}50x-140=25x+24\\-50x+140=25x+24\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{164}{25}\\x=\frac{116}{75}\end{cases}}\)

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

=> \(\orbr{\begin{cases}\frac{7}{5}x+\frac{2}{3}=\frac{4}{3}x-\frac{1}{4}\\-\frac{7}{5}x-\frac{2}{3}=\frac{4}{3}x-\frac{1}{4}\end{cases}}\)

=> \(\orbr{\begin{cases}x=-\frac{55}{4}\\x=-\frac{25}{164}\end{cases}}\)

Bài 2 : a. |2x - 5| = x + 1

 TH1 : 2x - 5 = x + 1

    => 2x - 5 - x = 1

    => 2x - x - 5 = 1

    => 2x - x = 6

    => x = 6

TH2 : -2x + 5 = x + 1

   => -2x + 5 - x = 1

   => -2x - x + 5 = 1

   => -3x = -4

   => x = 4/3

Ba bài còn lại tương tự

cho mình

\(\frac{4x-3}{3x+1}=\frac{5}{7}\)

=> \(7(4x-3)=5(3x+1)\)

=> \(28x-21=15x+5\)

=> \(28x-21-15x=5\)

=> \(28x-15x-21=5\)

=> \(28x-15x=26\)

=> \(13x=26\)

=> \(x=2\)

a) \(\frac{3x}{5}=\frac{1-4x}{3}\)

=> 3x . 3 = 5.(1-4x)

=>  9x    =     5 -20x

=> 9x + 20x =5

=> 29x        =5

=> x =\(\frac{5}{29}\)

b)\(\frac{x}{5}=\frac{15}{3x}\)

=>3x . x = 15 . 5

=> \(3x^2\)=75

=>  \(x^2\)=25

=> x       = \(\sqrt{25}\)

=>x         = 5                 CHÚC BẠN HỌC TỐT 

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

=>3x.3=5(1-4x)

=>9x=5-20x

=>9x+20x=5

=>29x=5

=>x=5/29

VẬy,...

\(\left(4x+3\right)^2=\frac{2}{3}:6\)

\(\left(4x+3\right)^2=\frac{1}{9}\)

\(\left(4x+3\right)^2=\left(\frac{1}{3}\right)^2\)

\(\Rightarrow4x+3=\frac{1}{3}\)

\(4x=-\frac{8}{3}\)

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

dòng thứ 4 phải ra 2 trường hợp chứ

a)\(\left(\frac{4}{5}\right)^{2x+7}=\left(\frac{4}{5}\right)^4\)

=> 2x + 7 = 4 

     2x        = 4 - 7 

     2x        = -3

       x        = -3 : 2

       x         = -1,5

   Vậy x = -1,5

tổng 2 số là 150, tổng của 1/6 số này và 1/9 số kia = 18. Tìm 2 số đó

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

\(2x^2-\frac{1}{2}x+2x^2-10x-3x=7\)

\(\frac{-27}{2}x=7\)

\(x=\frac{-14}{27}\)

Vậy,....

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

\(\Leftrightarrow\left(-2x^2\right)+\left(-\frac{1}{2}x\right)+2x^2-10x=3x+7\)

\(\Leftrightarrow-\frac{1}{2}x-10x=3x+7\)

\(\Leftrightarrow-\frac{1}{2}x-\frac{20}{2}x=3x+7\)

\(\Leftrightarrow-\frac{21}{2}x=3x+7\)

Từ đây tính nốt nhé!

\(\frac{3x-7}{5}=\frac{2x-1}{3}\)

\(\Leftrightarrow9x-21=10x-5\)

\(\Leftrightarrow-x=16\Leftrightarrow x=-16\)

\(\frac{4x-7}{12}-x=\frac{3x}{8}\)

\(\Leftrightarrow\frac{4x-7-12x}{12}=\frac{3x}{8}\)

\(\Leftrightarrow\frac{-7-8x}{12}=\frac{3x}{8}\)

\(\Leftrightarrow-56-64x=36x\)

\(\Leftrightarrow-56=100x\Leftrightarrow x=\frac{-14}{25}\)

\(\frac{x-2009}{1234}+\frac{x-2009}{5678}-\frac{x-2009}{197}=0\)

\(\Leftrightarrow\left(x-2019\right)\left(\frac{1}{1234}+\frac{1}{5678}-\frac{1}{197}\right)=0\)

Vì \(\left(\frac{1}{1234}+\frac{1}{5678}-\frac{1}{197}\right)\ne0\)nên x - 2019 = 0

Vậy x = 2019

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

\(\Leftrightarrow10x-16=3-9x\)

\(\Leftrightarrow19x=19\Leftrightarrow x=1\)

\(\frac{x-5}{6}-\frac{x-9}{4}=\frac{5x-3}{8}+2\)

\(\Rightarrow\frac{4x-20-6x+54}{24}=\frac{5x-3+16}{8}\)

\(\Rightarrow\frac{-2x+34}{24}=\frac{5x+13}{8}\)

\(\Rightarrow-16x-272=120x+312\)

\(\Leftrightarrow-136x=584\Leftrightarrow x=\frac{-73}{17}\)

hai tk là 1 :vvv

ai quen thì kb cả 2 tk nhé

a) \(\frac{4x-7}{12}-x=\frac{3x}{8}\)

\(\Rightarrow\frac{4x-7-12x}{12}=\frac{3x}{8}\)

\(\Rightarrow\frac{-7-8x}{12}=\frac{3x}{8}\)

\(\Rightarrow-56-64x=36x\)

\(\Leftrightarrow100x=-56\Leftrightarrow x=\frac{-14}{25}\)