1.
$\huge \frac{6+25x}{15}-(x-1)=\frac{2x}{3}+\frac{7}{5}$
$\frac{6+25x}{15}-(x-1)=\frac{2x}{3}+\frac{7}{5}\;/\times15$
$6+25x-15(x-1)=10x+21$
$6+25x-15x+15=10x+21$
$25x-15x-10x=21-15-6$
$0=0$
$x=R$
2.
$\huge x-\frac{1-\frac{3x}{2}}{4}-\frac{2-\frac{x}{4}}{3}=2$
$x-\frac{1-\frac{3x}{2}}{4}-\frac{2-\frac{x}{4}}{3}=2\;/\times12$
$12x-3(1-\frac{3x}{2}-4(2-\frac{x}{4}=24$
$12x-3+\frac{9x}{2}-8+x=24\;/times2$
$26x+9x=70$
$35x=70$
$x=2$
3.
$\huge x-\left(\frac{x}{2}-\frac{3+x}{4}\right)\times\frac{1}{2}=\left[3-(1-\frac{6-x}{3})\times\frac{1}{2}\right]\times\frac{1}{2}+\frac{3}{2}$
$x-\left(\frac{x}{4}-\frac{3+x}{8}\right)=\left[3-(\frac{1}{2}1-\frac{6-x}{6})\right]\times\frac{1}{2}+\frac{3}{2}$
$x-\frac{x}{4}+\frac{3+x}{8}=\frac{3}{2}-\frac{1}{4}+\frac{6-x}{12}+\frac{3}{2}$
$\frac{8x-2x+3+x}{8}=\frac{18-3+6-x+18}{12}$
$\frac{7x+3}{8}=\frac{39-x}{12}\;/\times24$
$21x+9=78-2x$
$23x=69$
$x=3$
4.
$\huge 4(x+1)-\frac{5x+1}{2}-\frac{5x-11}{4}=\frac{x-1}{3}-\frac{2(1-4x)}{9}$
$4(x+1)-\frac{5x+1}{2}-\frac{5x-11}{4}=\frac{x-1}{3}-\frac{2(1-4x)}{9}\;/\times36$
$144(x+1)-18(5x+1)-9(5x-11)=12(x-1)-8(1-4x)$
$144x+144-90x-18-45x+99=12x-12-8+32x$
$9x+225=44x-20$
$-35x=-245$
$x=7$
5.
$\huge 2\left(\frac{3x-1}{4}-\frac{3}{2}\right)-\left(\frac{1+x}{4}+1\right)=\frac{1+5x}{7}-\frac{3}{2}(x+1)$
$\frac{3x-1}{2}-3-\frac{1+x}{4}-1=\frac{1+5x}{7}-\frac{3x+3}{2}$
$\frac{3x-1}{2}-\frac{1+x}{4}-4=\frac{1+5x}{7}-\frac{3x+3}{2}\;/\times28$
$14(3x-1)-7(1+x)-112=4(1+5x)-14(3x+3)$
$42x-14-7-7x-112=4+20x-42x-42$
$35x-133=-22x-38$
$57x=95$
$x=\frac{95}{57}=\frac{5}{3}$
6.
$\huge \frac{2x-1}{2}+\frac{x}{6}<\frac{7x+2}{3}-\frac{x+3}{4}$
$6(2x-1)+2x<4(7x+2)-3(x+3)$
$12x-6+2x<28x+8-3x-9$
$14x-6<25x-1$
$-11x<5$
$x>-\frac{5}{11}$
$x\in\mathbb{R}$
$K=(-\frac{5}{11};\infty)$
7.
$\huge \frac{2x-1}{5}-\frac{3-2x}{4}<3-\frac{x-1}{2}$
$\frac{2x-1}{5}-\frac{3-2x}{4}<3-\frac{x-1}{2}\;/\times 20$
$4(2x-1)-5(3-2x)<60-10(x-1)$
$8x-4-15+10x<60-10x+10$
$18x-19<-10x+70$
$28x<89$
$x<3\frac{5}{28}$
$x\in\mathbb{N}$
$K=\left \{1;2;3 \right \}$
8.
$\huge \frac{4x-3}{5}-\frac{3x-4}{2}+\frac{2x-5}{3}<0$
$\frac{4x-3}{5}-\frac{3x-4}{2}+\frac{2x-5}{3}<0\;/\times 30$
$6(4x-3)-15(3x-4)+10(2x-5)<0$
$24x-18-45x+60+20x-50<0$
$-x-8<0$
$x>-8$
$K=\left \{x\in\mathbb{Z}\wedge (-8;\infty)\right \}$
9.
$\huge \frac{2x-1}{3}-\frac{x+3}{2}<3-\frac{x-2}{3}$
$\frac{2x-1}{3}-\frac{x+3}{2}<3-\frac{x-2}{3}\;/\times 6$
$2(2x-1)-3(x+3)<18-2(x-2)$
$4x-2-3x-9<18-2x+4$
$3x<33$
$x<11$
$x\in\mathbb{N}$
$K=\left \{1;2;3;4;5;6;7;8;9;10 \right \}$
10.
$\huge \frac{x+1}{5}-\frac{x-1}{2}-3<\frac{2x-1}{2}$
$\frac{x+1}{5}-\frac{x-1}{2}-3<\frac{2x-1}{2}\;/\times 10$
$2(x+1)-5(x-1)-30<5(2x-1)$
$2x+2-5x+5-30<10x-5$
$-3x-23<10x-5$
$-13x<18$
$x>-\frac{18}{13}$
$x>-1\frac{5}{13}$
$x\in\mathbb{Z^{-}}$
$K=\left \{-1 \right \}$