Question 138487
{{{((x+1))/3}}} = {{{(-x)/6}}}
:
The easiest way to solve these type of problems, where you have single faction on
each side of the equal sign, is to cross multiply, resulting in:
:
6(x+1) = 3(-x)
;
Multiply what's inside the brackets
6x + 6 = -3x 
:
Subtract 6 from both sides:
6x = -3x - 6
:
Add 3x to both sides
6x + 3x = -6
:
9x = -6
x = {{{(-6)/9}}}; divided both sides by 9
x = {{{-2/3}}}; reduced the fraction
:
:
Check solution in original equation:
{{{((x+1))/3}}} = {{{(-x)/6}}}
Substitute -2/3 for x
{{{(((-2/3)+1))/3}}} = {{{(-(-2/3))/6}}}
{{{((1/3))/3}}} = {{{((2/3))/6}}}; minus a minus is a plus
Invert the divisors and mult
{{{(1/3)*(1/3)}}} = {{{(2/3)*(1/6)}}}
{{{1/9}}} = {{{2/18}}}; equality reigns, confirms our solution