Ta có : 

\(\frac{3x-2}{5}\ge\frac{x}{2}+0,8\)

\(\Leftrightarrow x\ge12\)

và \(1-\frac{2x-5}{6}>\frac{3-x}{4}\)

\(\Leftrightarrow x< 13\)   \(x\in Z\)

\(\Rightarrow x=12\)

b, \(\frac{3x-2}{5}\ge\frac{x+1,6}{2}\)

=> \(6x-4\ge5x+8\)

=> \(x-12\ge0\)

=> \(x\ge12\)

bpt 2: \(\frac{6-2x+5}{6}>\frac{3-x}{4}\)

=> \(\frac{11-2x}{6}>\frac{3-x}{4}\)

=> \(44-8x>18-6x\)

=> \(x< 13\)

Vậy để t/m cả 2 bpt thì : \(12\le x< 13\)

a, \(\frac{x^2+x^2-4}{x\left(x-2\right)}>2\) (Đk : \(x\ne\left(0;2\right)\))

=> \(2x^2-4>2x^2-4x\)

=> \(4x-4=4\left(x-1\right)>0\)

=> \(x>1\)(t/m) 

\(\frac{2x}{5}+\frac{3-2x}{3}\ge\frac{3x+2}{2}\)

\(\Leftrightarrow\)\(\frac{12x}{30}+\frac{10\left(3-2x\right)}{30}\ge\frac{15\left(3x+2\right)}{30}\)

\(\Leftrightarrow\)12x + 30 - 20x \(\ge\) 45x + 30

\(\Leftrightarrow\) 12x - 20x - 45x \(\ge\) -30 + 30

\(\Leftrightarrow\)- 53x \(\ge\)0

\(\Leftrightarrow\)x \(\le\)0

Vậy bất phương trình có nghiệm là : x \(\le0\)

b) \(1-\frac{2x-5}{6}>\frac{3-x}{4}\)

\(\Leftrightarrow\)\(\frac{12}{12}-\frac{2\left(2x-5\right)}{12}>\frac{3\left(3-x\right)}{12}\)

\(\Leftrightarrow\) 12 - 4x + 10 > 9 - 3x

\(\Leftrightarrow\)-4x + 3x > -12 - 10 + 9

\(\Leftrightarrow\)-x > -13

\(\Leftrightarrow\)x < 13

Vậy bất phương trình có nghiệm là : x < 13

\(a,3^x>\dfrac{1}{243}\\ \Leftrightarrow3^x>3^{-5}\\ \Leftrightarrow x>-5\\ b,\left(\dfrac{2}{3}\right)^{3x-7}\le\dfrac{3}{2}\\ \Leftrightarrow3x-7\le1\\ \Leftrightarrow3x\le8\\ \Leftrightarrow x\le\dfrac{8}{3}\\ c,4^{x+3}\ge32^x\\ \Leftrightarrow2^{2x+6}\ge2^{5x}\\ \Leftrightarrow2x+6\ge5x\\ \Leftrightarrow3x\le6\\ \Leftrightarrow x\le2\)

d, Điều kiện: x > 1

\(log\left(x-1\right)< 0\\ \Leftrightarrow x-1< 1\\ \Leftrightarrow1< x< 2\)

e, Điều kiện: \(x>\dfrac{1}{2}\)

\(log_{\dfrac{1}{5}}\left(2x-1\right)\ge log_{\dfrac{1}{5}}\left(x+3\right)\\ \Leftrightarrow2x-1\ge x+3\\ \Leftrightarrow x\ge4\)

f, Điều kiện: x > 4

\(ln\left(x+3\right)\ge ln\left(2x-8\right)\\ \Leftrightarrow x+3\ge2x-8\\\Leftrightarrow4< x\le11\)

\(\frac{3x-2}{5}\ge\frac{x}{2}+\frac{4}{5}\Leftrightarrow2\left(3x-2\right)\ge5x+8\)

\(\Leftrightarrow x\ge12\) (1)

\(1-\frac{2x-5}{6}>\frac{3-x}{4}\Leftrightarrow12-2\left(2x-5\right)>3\left(3-x\right)\)

\(\Leftrightarrow22-4x>9-3x\Leftrightarrow x< 13\) (2)

Từ (1) và (2) \(\Rightarrow12\le x< 13\)

Mà \(x\in Z\Rightarrow x=12\)

\(a,\frac{2x}{5}+\frac{3-2x}{3}\ge\frac{3x+2}{2}\)

\(\Leftrightarrow\frac{12x}{30}+\frac{10\left(3-2x\right)}{30}\ge\frac{15\left(3x+2\right)}{30}\)

\(\Leftrightarrow\frac{12x+30-20x}{30}\ge\frac{45x+30}{30}\)

\(\Leftrightarrow-8x+30\ge45x+30\)

\(\Leftrightarrow-8x-45x\ge30-30\)

\(\Leftrightarrow-53x\ge0\)\(\Leftrightarrow x\le0\)

Vậy tập nghiệm của bất phương trình là S = {\(x\le0\)}.

\(b,1-\frac{2x-5}{6}>\frac{3-x}{4}\)

\(\Leftrightarrow\frac{12}{12}-\frac{2\left(2x-5\right)}{12}>\frac{3\left(3-x\right)}{12}\)

\(\Leftrightarrow\frac{12-4x+10}{12}>\frac{9-3x}{12}\)

\(\Leftrightarrow12-4x+10>9-3x\)

\(\Leftrightarrow22-4x>9-3x\)

\(\Leftrightarrow-4x+3x>9-22\)

\(\Leftrightarrow-x>-13\)\(\Leftrightarrow x< 13\)

Vậy tập nghiệm của bất phương trình là S = {x<13}.

1)

a) \(\frac{x+5}{3x-6}-\frac{1}{2}=\frac{2x-3}{2x-4}< =>\frac{2\left(x+5\right)}{2\left(3x-6\right)}-\frac{3x-6}{2\left(3x-6\right)}=\frac{3\left(2x-3\right)}{3\left(2x-4\right)}.\)

(đk:x khác \(\frac{1}{2}\))

\(\frac{2x+10}{6x-12}-\frac{3x-6}{6x-12}=\frac{6x-9}{6x-12}< =>2x+10-3x+6=6x-9< =>x=\frac{25}{7}\)

Vậy x=\(\frac{25}{7}\)

b) /7-2x/=x-3 \(x\ge\frac{7}{2}\)

(đk \(x\ge3,\frac{7}{2}< =>x\ge\frac{7}{2}\))

\(\Rightarrow\orbr{\begin{cases}7-2x=x-3\\7-2x=-\left(x-3\right)\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{10}{3}\left(< \frac{7}{2}\Rightarrow l\right)\\x=4\left(tm\right)\end{cases}}}\)

Vậy x=4

2)

\(\frac{x-1}{2}+\frac{x-2}{3}+\frac{x-3}{4}>\frac{x-4}{5}+\frac{x-5}{6}\)

\(\Leftrightarrow\frac{30\left(x-1\right)}{60}+\frac{20\left(x-2\right)}{60}+\frac{15\left(x-3\right)}{60}-\frac{12\left(x-4\right)}{60}-\frac{10\left(x-5\right)}{60}>0\)

\(\Leftrightarrow30x-30+20x-40+15x-45-12x+48-10x+50>0\Leftrightarrow43x-17>0\Leftrightarrow x>\frac{17}{43}\)