13: \(\dfrac{2x-1}{3}-\dfrac{x+2}{2}>=\dfrac{5x+4}{6}\)
=>\(\dfrac{2\cdot\left(2x-1\right)-3\left(x+2\right)}{6}>=\dfrac{5x+4}{6}\)
=>2(2x-1)-3(x+2)>=5x+4
=>4x-2-3x-6>=5x+4
=>x-8>=5x+4
=>-4x>=12
=>x<=-3
14: \(\dfrac{2x+3}{-4}>=\dfrac{4-x}{-6}+1\)
=>\(\dfrac{-2x-3}{4}>=\dfrac{x-4}{6}+1\)
=>\(\dfrac{3\left(-2x-3\right)}{12}>=\dfrac{2\left(x-4\right)+12}{12}\)
=>3(-2x-3)>=2(x-4)+12
=>-6x-9>=2x-8+12
=>-6x-9>=2x+4
=>-8x>=13
=>\(x< =-\dfrac{13}{8}\)
15: \(\dfrac{7x+3}{4}-\dfrac{2-5x}{3}< =\dfrac{2x-7}{2}+1\)
=>\(\dfrac{3\left(7x+3\right)-4\left(2-5x\right)}{12}< =\dfrac{6\left(2x-7\right)}{12}+\dfrac{12}{12}\)
=>\(3\left(7x+3\right)-4\left(2-5x\right)< =6\left(2x-7\right)+12\)
=>\(21x+9-8+20x< =12x-42+12\)
=>41x+1<=12x-30
=>29x<=-31
=>\(x< =-\dfrac{31}{29}\)
16: \(\dfrac{x-3}{3}-\dfrac{x-4}{4}>=\dfrac{2x-3}{8}\)
=>\(\dfrac{8\left(x-3\right)}{24}-\dfrac{6\left(x-4\right)}{24}>=\dfrac{3\left(2x-3\right)}{24}\)
=>8(x-3)-6(x-4)>=3(2x-3)
=>8x-24-6x+24>=6x-9
=>2x-6x>=-9
=>-4x>=-9
=>4x<=9
=>\(x< =\dfrac{9}{4}\)
\(13)\dfrac{2x-1}{3}-\dfrac{x+2}{2}\ge\dfrac{5x+4}{6}\\ \Leftrightarrow\dfrac{2\left(2x-1\right)}{6}-\dfrac{3\left(x+2\right)}{6}\ge\dfrac{5x+4}{6}\\ \Leftrightarrow2\left(2x-1\right)-3\left(x+2\right)\ge5x+4\\ \Leftrightarrow4x-2-3x-6\ge5x+4\\ \Leftrightarrow x-8\ge5x+4\\ \Leftrightarrow5x-x\le-8-4\\ \Leftrightarrow4x\le-12\\ \Leftrightarrow x\le-\dfrac{12}{4}=-3\\14) \dfrac{2x+3}{-4}\ge\dfrac{4-x}{-6}+1\\ \Leftrightarrow\dfrac{-3\left(2x+3\right)}{12}\ge\dfrac{2\left(x-4\right)}{12}+\dfrac{6}{6}\\ \Leftrightarrow-3\left(2x+3\right)\ge2\left(x-4\right)+6\\ \Leftrightarrow-6x-9\ge2x-8+6\\ \Leftrightarrow-6x-9\ge2x-2\\ \Leftrightarrow2x+6x\le-9+2\\ \Leftrightarrow8x\le-7\\ \Leftrightarrow x\le-\dfrac{7}{8}\)
\(15.\dfrac{7x+3}{4}-\dfrac{2-5x}{3}\le\dfrac{2x-7}{2}+1\\ \Leftrightarrow\dfrac{3\left(7x+3\right)}{12}+\dfrac{4\left(5x-2\right)}{12}\le\dfrac{6\left(2x-7\right)}{12}+\dfrac{12}{12}\\ \Leftrightarrow3\left(7x+3\right)+4\left(5x-2\right)\le6\left(2x-7\right)+12\\ \Leftrightarrow21x+9+20x-8\le12x-42+12\\ \Leftrightarrow41x+1\le12x-30\\ \Leftrightarrow41x-12x\le-30-1\\ \Leftrightarrow29x\le-31\\ \Leftrightarrow x\le-\dfrac{31}{29}\\ 16.\dfrac{x-3}{3}-\dfrac{x-4}{4}\ge\dfrac{2x-3}{8}\\ \Leftrightarrow\dfrac{8\left(x-3\right)}{24}-\dfrac{6\left(x-4\right)}{24}\ge\dfrac{3\left(2x-3\right)}{24}\\ \Leftrightarrow8\left(x-3\right)-6\left(x-4\right)\ge3\left(2x-3\right)\\ \Leftrightarrow8x-24-6x+24\ge6x-9\\ \Leftrightarrow2x\ge6x-9\\ \Leftrightarrow6x-2x\le9\\ \Leftrightarrow4x\le9\\ \Leftrightarrow x\le\dfrac{9}{4}\)
