Question 57054
{{{3(x - 2y) = -12(x + 2y)}}}
use the distributive law to factor the equation
{{{3x - 6y = -12x - 24y}}}
add 24y to both sides
{{{3x - 6y + 24y = -12x - 24y + 24y}}}
{{{3x - 6y + 24y = -12x}}}
subtract 3x from both sides
{{{3x - 3x -6y  + 24y = -12x - 3x}}}
{{{-6y + 24y = - 12x - 3x}}}
{{{18y = -15x}}}
divide both sides by 18
{{{y = (-15/18)*x}}}
simplify -15/18 to -5/6
{{{y = (-5/6)*x}}} answer
you can check this answer by plugging it back into the original equation
{{{3(x - 2((-5/6)*x)) = -12(x + 2((-5/6)*x))}}}
{{{3(x + (10/6)*x) = -12(x - (10/6)*x)}}}
simplify 10/6 to 5/3
{{{3(x + (5/3)*x) = -12(x - (5/3)*x)}}}
note that x = (3/3)*x
{{{3((3/3)*x + (5/3)*x) = -12((3/3)*x - (5/3)*x)}}}
{{{3((8/3)*x) = -12((-2/3)*x)}}}
{{{8x = (24/3)*x}}}
{{{8x = 8x}}}
OK
checking answers is always a good idea when you have the time