$\begin{array}{l}\left|5x-4\right|=4-5x\left(8\right)\\ +)x\ge \frac{4}{5}\Rightarrow \left(8\right)\iff 5x-4=4-5x\iff x=\frac{4}{5}(tm)\\ +)x<\frac{4}{5}\Rightarrow \left(8\right)\iff 4-5x=4-5x\iff x\in ℝ/x<\frac{4}{5}S=\left\{x/x\le \frac{4}{5}\right\}\end{array}$

$\begin{array}{l}\left|x+5\right|=3x-2\left(9\right)\\ +)x\ge -5\Rightarrow \left(9\right)\iff x+5=3x-2\iff x=\frac{7}{2}(tm)\\ +)x<-5\Rightarrow \left(9\right)\iff -x-5=3x-2\iff x=-\frac{3}{4}(ktm)S=\left\{\frac{7}{2}\right\}\end{array}$

$\begin{array}{l}\left|9+x\right|=2x\left(10\right)\\ +)x\ge -9\Rightarrow \left(10\right)\iff 9+x=2x\iff x=9(tm)\\ +)x<-9\Rightarrow \left(10\right)\iff -9-x=2x\iff x=-3(ktm)S=\left\{9\right\}\end{array}$

$\begin{array}{l}\left|x+6\right|=2x+9\left(11\right)\\ +)x\ge -6\Rightarrow \left(11\right)\iff x+6=2x+9\iff x=-3(tm)\\ +)x<-6\Rightarrow \left(11\right)\iff -x-6=2x+9\iff x=-5(ktm)S=\left\{-3\right\}\end{array}$

$\begin{array}{l}\left|2x-3\right|=2x-3\left(12\right)\\ +)x\ge \frac{3}{2}\Rightarrow \left(12\right)\iff 2x-3=2x-3\iff x\in R/x\ge \frac{3}{2}\\ +)x<\frac{3}{2}\Rightarrow \left(12\right)\iff 3-2x=2x-3\iff x=\frac{3}{2}(ktm)S=\left\{x/x\ge \frac{3}{2}\right\}\end{array}$

Với $x\ge -2\Rightarrow \left(13\right)\iff 4+2x=-4x\iff x=-\frac{2}{3}\left(tm\right)$

Với $x<-2\Rightarrow \left(13\right)\iff -4-2x=-4x\iff x=2\left(ktm\right)$

Vậy $S=\left\{-\frac{2}{3}\right\}$

Với $x\ge 0\Rightarrow \left(14\right)\iff 5x=3x-2\iff x=-1\left(ktm\right)$

Với $x<0\Rightarrow \left(14\right)\iff -5x=3x-2\iff x=\frac{1}{4}\left(ktm\right)$

Vậy $S=\varnothing$

Với $x\ge 0\Rightarrow \left(15\right)\iff \mathrm{2,5}x=x-12\iff x=-8\left(ktm\right)$

$+)x<0\Rightarrow \left(15\right)\iff -\mathrm{2,5}x=x-12\iff x=\frac{24}{7}(ktm)$

$S=\varnothing$Vậy 

Với $x\ge 0\Rightarrow \left(16\right)\iff 5x-3x-2=0\iff x=1\left(tm\right)$

Với $x<0\Rightarrow \left(16\right)\iff -5x-3x-2=0\iff x=-\frac{1}{4}\left(tm\right)$

Vậy $S=\left\{1;-\frac{1}{4}\right\}$

Với $x\ge 0\Rightarrow \left(17\right)\iff 2x+x-5x-3=0\iff x=-\frac{3}{2}\left(ktm\right)$

Với $x<0\Rightarrow \left(17\right)\iff -2x+x-5x-3=0\iff x=-\frac{1}{2}\left(tm\right)$

Vậy $S=\left\{-\frac{1}{2}\right\}$

Với $x\ge 5\Rightarrow \left(18\right)\iff x-5=7\iff x=12\left(tm\right)$

Với $x<5\Rightarrow \left(18\right)\iff 5-x=7\iff x=-2\left(tm\right)$

Vậy $S=\left\{12;-2\right\}$

Với $x\ge 6\iff \left(19\right)\iff -6+x=3\iff x=9\left(tm\right)$

Với $x<6\Rightarrow \left(19\right)\iff 6-x=3\iff x=3\left(tm\right)$

Vậy $S=\left\{9;3\right\}$

$\begin{array}{l}\left|x+5\right|=3x-2\left(20\right)\\ +)x\ge -5\Rightarrow \left(20\right)\iff x+5=3x-2\iff x=\frac{7}{2}(tm)\\ +)x<-5\Rightarrow \left(20\right)\iff -x-5=3x-2\iff x=\frac{-3}{4}(ktm)S=\left\{\frac{7}{2}\right\}\end{array}$

$\begin{array}{l}\left|2x-1\right|-3x=6\left(21\right)\\ +)x\ge \frac{1}{2}\Rightarrow \left(21\right)\iff 2x-3-3x=6\iff x=-7(ktm)\\ +)x<\frac{1}{2}\Rightarrow \left(21\right)\iff 1-2x-3x=6\iff x=-1(tm)S=\left\{-1\right\}\end{array}$

$\begin{array}{l}\left|-2x\right|-3x=4\left(22\right)\\ +)x\ge 0\Rightarrow \left(22\right)\iff 2x-3x=4\iff x=-4(ktm)\\ +)x<0\Rightarrow \left(22\right)\iff -2x-3x=4\iff x=-\frac{4}{5}(tm)S=\left\{-\frac{4}{5}\right\}\end{array}$

$\begin{array}{l}\left|3x-1\right|=x-2\left(23\right)\\ +)x\ge \frac{1}{3}\Rightarrow \left(23\right)\iff 3x-1=x-2\iff x=-\frac{1}{2}(ktm)\\ +)x<\frac{1}{3}\Rightarrow \left(23\right)\iff 1-3x=x-2\iff x=\frac{3}{4}(ktm)\end{array}$

$\begin{array}{l}\left|x+2\right|=2x-10\left(24\right)\\ +)x\ge -2\Rightarrow \left(24\right)\iff x+2=2x-10\iff x=12(tm)\\ +)x<2\Rightarrow \left(24\right)\iff -x-2=2x-10\iff x=\frac{8}{3}(ktm)\end{array}$

$\begin{array}{l}\left|x-3\right|=5\left(25\right)\\ +)x\ge 3\Rightarrow \left(25\right)\iff x-3=5\iff x=8(tm)\\ +)x<3\Rightarrow \left(25\right)\iff 3-x=5\iff x=-2(tm)S=\left\{8;-2\right\}\end{array}$

$\begin{array}{l}\left|2x+1\right|=\left|x+1\right|\\ \Rightarrow \left[\begin{array}{l}2x+1=x+1\\ 2x+1=-x-1\end{array}\right.\iff \left[\begin{array}{l}x=0\\ x=-\frac{2}{3}\end{array}\right.S=\left\{0;\frac{-2}{3}\right\}\end{array}$

$\begin{array}{l}\left|-5x\right|=3x-16\left(27\right)\\ +)x\ge 0\Rightarrow \left(27\right)\iff 5x=3x-16\iff x=-8(ktm)\\ +)x<0\Rightarrow \left(27\right)\iff -5x=3x-16\iff x=2(ktm)S=\varnothing \end{array}$

$\begin{array}{l}\left|2x+1\right|-\left|5x-2\right|=3\left(28\right)\\ *)x<-\frac{1}{2}\Rightarrow \left(28\right)\iff -2x-1-2+5x=3\iff x=2(ktm)\\ *)-\frac{1}{2}\le x\le \frac{2}{5}\Rightarrow \left(28\right)\iff 2x+1-2+5x=3\iff x=\frac{4}{7}(ktm)\\ *)x>\frac{2}{5}\Rightarrow \left(28\right)\iff 2x+1-5x+2=3\iff x=0(ktm)S=\varnothing \end{array}$

$\begin{array}{l}\left|2-3x\right|-4x=5\left(29\right)\\ +)x\ge \frac{3}{2}\Rightarrow \left(29\right)\iff 2x-3-4x=5\iff x=-4(ktm)\\ +)x<\frac{3}{2}\Rightarrow \left(29\right)\iff 3-2x-4x=5\iff x=-\frac{1}{3}(tm)S=\left\{-\frac{1}{3}\right\}\end{array}$

$\begin{array}{l}{\left(x+1\right)}^2-\left|5-3x\right|-x=x\left(x+2\right)+4\\ \iff x^2+2x+1-\left|5-3x\right|-x=x^2+2x+4\\ \iff \left|5-3x\right|=-3-x\\ +)x\ge \frac{5}{3}\Rightarrow 5-3x=-3-x\iff x=4(tm)\\ +)x<-\frac{5}{3}\Rightarrow 3x-5=-3-x\iff x=\frac{1}{2}(ktm)S=\left\{4\right\}\end{array}$

$\begin{array}{l}\left|2x-3\right|=x-5\left(31\right)\\ +)x\ge \frac{3}{2}\Rightarrow \left(31\right)\iff 2x-3=x-5\iff x=-2(ktm)\\ +)x<\frac{3}{2}\Rightarrow \left(31\right)\iff 3-2x=x-5\iff x=\frac{8}{3}(ktm)S=\varnothing \end{array}$

$\begin{array}{l}\left|3x+2\right|=x+1\left(32\right)\\ +)x\ge \frac{-2}{3}\Rightarrow \left(32\right)\iff 3x+2=x+1\iff x=-\frac{1}{2}(tm)\\ +)x<-\frac{2}{3}\Rightarrow \left(32\right)\iff -3x-3=x+1\iff x=-1(ktm)S=\left\{-\frac{1}{2}\right\}\end{array}$

$\begin{array}{l}\left|2x+1\right|=7-x\left(33\right)\\ +)x\ge -\frac{1}{2}\Rightarrow \left(33\right)\iff 2x+1=7-x\iff x=2(tm)\\ +)x<-\frac{1}{2}\Rightarrow \left(33\right)\iff -2x-1=7-x\iff x=-8(tm)S=\left\{2;-8\right\}\end{array}$

$\begin{array}{l}\left|2x-5\right|=x+1\left(34\right)\\ +)x\ge \frac{5}{2}\Rightarrow \left(34\right)\iff 2x-5=x+1\iff x=6(tm)\\ +)x<\frac{5}{2}\Rightarrow \left(34\right)\iff 5-2x=x+1\iff x=\frac{4}{3}(tm)S=\left\{6;\frac{4}{3}\right\}\end{array}$

$\begin{array}{l}\left|6x-2\right|=3x-4\left(35\right)\\ +)x\ge \frac{1}{3}\Rightarrow \left(35\right)\iff 6x-2=3x-4\iff x=-\frac{2}{3}(ktm)\\ +)x<\frac{1}{3}\Rightarrow \left(35\right)\iff 2-6x=3x-4\iff x=\frac{2}{3}(ktm)S=\varnothing \end{array}$

$\begin{array}{l}\left|3x-2\right|=x-2\left(36\right)\\ +)x\ge \frac{2}{3}\Rightarrow \left(36\right)\iff 3x-2=x-2\iff x=0(ktm)\\ +)x<\frac{2}{3}\Rightarrow \left(36\right)\iff 2-3x=x-2\iff x=1(ktm)S=\varnothing \end{array}$

$\begin{array}{l}\left|2x+1\right|=7-x\left(37\right)\\ +)x\ge -\frac{1}{2}\Rightarrow \left(37\right)\iff 2x+1=7-x\iff x=2(tm)\\ +)x<-\frac{1}{2}\Rightarrow \left(37\right)\iff -2x-1=7-x\iff x=-8(tm)S=\left\{2;-8\right\}\end{array}$

$\begin{array}{l}\left|2-x\right|=2x+1\left(38\right)\\ +)x\ge 2\Rightarrow \left(38\right)\iff x-2=2x+1\iff x=-3(ktm)\\ +)x<2\Rightarrow \left(38\right)\iff 2-x=2x+1\iff x=\frac{1}{3}(tm)S=\left\{\frac{1}{3}\right\}\end{array}$

$\begin{array}{l}\left|2x-1\right|=x-3\left(39\right)\\ +)x\ge \frac{1}{2}\Rightarrow \left(39\right)\iff 2x-1=x-3\iff x=-2(ktm)\\ +)x<\frac{1}{2}\Rightarrow \left(39\right)\iff 1-2x=x-3\iff x=\frac{4}{3}(ktm)S=\varnothing \end{array}$

$\begin{array}{l}2\left|x-1\right|=x+2\left(40\right)\\ +)x\ge 1\Rightarrow \left(40\right)\iff 2\left(x-1\right)=x+2\iff x=4(tm)\\ +)x<1\Rightarrow \left(40\right)\iff 2\left(1-x\right)=x+2\iff x=0(tm)S=\left\{4;0\right\}\end{array}$

$\begin{array}{l}\left|x-1\right|=2x-1\left(41\right)\\ +)x\ge 1\Rightarrow \left(41\right)\iff x-1=2x-1\iff x=0(ktm)\\ +)x<1\Rightarrow \left(41\right)\iff 1-x=2x-1\iff x=\frac{2}{3}(tm)S=\left\{\frac{2}{3}\right\}\end{array}$

$\begin{array}{l}\left|x-2\right|=2-x\left(42\right)\\ +)x\ge 2\Rightarrow \left(42\right)\iff x-2=2-x\iff x=2(tm)\\ +)x<2\Rightarrow \left(42\right)\iff 2-x=2-x\Rightarrow x\in ℝS=\left\{x/x\le 2\right\}\end{array}$

$\begin{array}{l}\left|3x-5\right|=2x+1\left(43\right)\\ +)x\ge \frac{5}{3}\iff \left(43\right)\iff 3x-5=2x+1\iff x=6(tm)\\ +)x<\frac{5}{3}\iff \left(43\right)\iff 5-3x=2x+1\iff x=\frac{4}{5}(tm)S=\left\{6;\frac{4}{5}\right\}\end{array}$

$\begin{array}{l}\left|7x-4\right|=\left|3x-4\right|\\ \Rightarrow \left[\begin{array}{l}7x-4=3x-4\\ 7x-4=4-3x\end{array}\right.\iff \left[\begin{array}{l}4x=0\\ 10x=8\end{array}\right.\iff \left[\begin{array}{l}x=0\\ x=\frac{4}{5}\end{array}\right.S=\left\{0;\frac{4}{5}\right\}\end{array}$

$\begin{array}{l}\left|2x+1\right|=\left|x\right|\\ \Rightarrow \left[\begin{array}{l}2x+1=x\\ 2x+1=-x\end{array}\right.\iff \left[\begin{array}{l}x=-1\\ x=-\frac{1}{3}\end{array}\right.S=\left\{-1;-\frac{1}{3}\right\}\end{array}$

$\begin{array}{l}\left|3x+4\right|=\left|x-2\right|\\ \Rightarrow \left[\begin{array}{l}3x+4=x-2\\ 3x+4=2-x\end{array}\right.\iff \left[\begin{array}{l}2x=-6\\ 4x=-2\end{array}\right.\iff \left[\begin{array}{l}x=-3\\ x=-\frac{1}{2}\end{array}\right.S=\left\{-3;-\frac{1}{2}\right\}\end{array}$

$\begin{array}{l}\left|x-3\right|=\left|2x-1\right|\\ \Rightarrow \left[\begin{array}{l}x-3=2x-1\\ x-3=1-2x\end{array}\right.\iff \left[\begin{array}{l}x=-2\\ x=\frac{4}{3}\end{array}\right.S=\left\{-2;\frac{4}{3}\right\}\end{array}$

$\begin{array}{l}\left|2x+5\right|=\left|3x-2\right|\\ \Rightarrow \left[\begin{array}{l}2x+5=3x-2\\ 2x+5=2-3x\end{array}\right.\iff \left[\begin{array}{l}x=7\\ x=-\frac{3}{5}\end{array}\right.S=\left\{7;\frac{-3}{5}\right\}\end{array}$

$\begin{array}{l}\left|x-3\right|=\left|2x-1\right|\\ \Rightarrow \left[\begin{array}{l}x-3=2x-1\\ x-3=1-2x\end{array}\right.\iff \left[\begin{array}{l}x=-2\\ x=\frac{4}{3}\end{array}\right.S=\left\{-2;\frac{4}{3}\right\}\end{array}$