Question

1) x-(12x+1)/3=2x+1-(15x+4)/3


2) (3(x-3))/2+2x/3-2x=3(2x-1)/9-1/6




3) (x-2)/(3-x)=5/4

Answer 1

Explicación paso a paso:

a)

$x-\frac{(12x+1)}{3} =2x+1-\frac{(15x+4)}{3} \\\\x-4x-\frac{1}{3}=2x+1-5x-\frac{4}{3} \\\\x-4x-2x+5x=1-\frac{4}{3} +\frac{1}{3} \\\\-6x+6x=1-\frac{3}{3} \\\\0x=1-1\\\\0=0$

b)

$\frac{(3(x-3))}{2} +\frac{2x}{3}-2x=\frac{3(2x-1)}{9}-\frac{1}{6}\\\\\frac{3x-9}{2}+\frac{2x}{3}-2x=\frac{6x-3}{9}-\frac{1}{6} \\\\\frac{3x}{2}-\frac{9}{2}+\frac{2x}{3}-2x=\frac{6x}{9}-\frac{3}{9}-\frac{1}{6}\\\\\frac{3x}{2}+\frac{2x}{3}-\frac{2x}{3}-2x=\frac{9}{2}-\frac{1}{3}-\frac{1}{6}\\\\\frac{3x}{2}-2x=\frac{18-2-1}{6} \\\\\frac{3x-4x}{2} =\frac{15}{6} \\\\6(3x-4x)=2*15\\\\6(-x)=30\\\\-x=\frac{30}{6}\\-x=5\\\\x=-5$

c)

$\frac{(x-2)}{(3-x)} =\frac{5}{4} \\\\4*(x-2)=5*(3-x)\\\\4x-8=15-5x\\\\4x+5x=15+8\\\\9x=23\\\\x=\frac{23}{9}$