[tex]a)\\\\ \frac{ 2x+3}{5} =\frac{ 2-x }{3} - x \ \ |*15\\\\3(2x+3)=5(2-x)-15x\\\\6x+9=10-5x-15x\\\\6x+9=10-20x\\\\6x+20x= 10-9\\\\26x=1\ \ |:26\\\\x=\frac{1}{26}[/tex]
[tex]b)\\\\ \frac{ x+1}{2}-\frac{x-1}{3} =\frac{1}{4} \ \ |*12\\\\ 6(x+1)-4(x-1)=3\\\\6x+6-4x+4=3\\\\2x=3-6-4\\\\2x=-7\ \ |:2\\\\x=-\frac{7}{2}=-3\frac{1}{2}[/tex]
[tex]c)\\\\ \frac{ 4x+7}{2}-\frac{5x-1}{6} = x+5\ \ |*6\\\\3(4x+7)-(5x-1)=6x+30\\\\12x+21-5x+1=6x+30\\\\7x+22=6x+30\\\\7x-6x=30-22\\\\x=8[/tex]
[tex]d)\\\\ \frac{ x+5}{4}-\frac{2x+1}{8}=\frac{1}{2}(2-x)\ \ |*8\\\\2(x+5) -(2x+1)=4(2-x)\\\\2x+10-2x-1=8-4x\\\\9=8 -4x\\\\4x=8-9\\\\4x=-1\ \ |:4\\\\x=-\frac{1}{4}[/tex]
