a) (3x - 5)/2 - (5x - 1)/10 = 0 /*10 5(3x - 5) - (5x - 1) = 0 15x - 25 - 5x + 1 = 0 10x = 24 /:10 x = 24/10 x = 2 4/10 x = 2 2/5 b) x/2= 2/5(4 - x) - 4 /*10 5x = 4(4 - x) - 40 5x = 16 - 4x - 40 5x + 4x = -24 9x = -24 /:9 x = - 2 2/3 c) (2x - 1)/5 - (x - 2)/2 = 0,7x /*10 2(2x - 1) - 5(x - 2) = 7x 4x - 2 - 5x + 10 = 7x -x - 7x = -8 -8x = -8 /:(-8) x = 1 d) 2x - 3x + 5/4 = - 1/4x - 1 /*4 8x - 12x + 5 = - x - 4 -4x + x = -4 - 5 -3x = -9 /:(-3) x = 3
[latex]a)\frac{3x-5}{2}-frac{5x-1}{10}=/*10\\10*frac{3x-5}{2}-10*frac{5x-1}{10}=0\\5(3x-5)-(5x-1)=0\\15x-25-5x+1=0\\15x-5x=25-1\\10x=24/:10\\x=frac{24}{10}\\x=2frac{4}{10}\\x=2frac{2}{5}[/latex] [latex]b)\frac{x}{2}=frac{2}{5}(4-x)-4/*10\\10*frac{x}{2}=10*frac{2}{5}(4-x)-40\\5x=4(4-x)-40\\5x=16-4x-40\\5x+4x=-24\\9x=-24/:9\\x=-frac{24}{9}\\x=-2frac{6}{9}\\x=-2frac{2}{3}[/latex] [latex]c)\frac{2x-1}{5}-frac{x-2}{2}=0,7x/*10\\10*frac{2x-1}{5}-10*frac{x-2}{2}=7x\\2(2x-1)-5(x-2)=7x\\4x-2-5x+10=7x\\4x-5x-7x=2-10\\-8x=-8/:(-8)\\x=1 [/latex] [latex]d)\2x-frac{3x+5}{4}=-frac{1}{4}x-1\\4*2x-4*frac{3x+5}{4}=4*-frac{1}{4}x-4*1\\8x-(3x+5)=-x-4\\8x-3x-5=-x-4\\8x-3x+x=-4+5\\6x=1/:6\\x=frac{1}{6}[/latex]
