Question 551678
2x+3 all over 5 - x-2 all over 4 = a half 
Assume the problem is
{{{((2x+3))/5}}} - {{{((x-2))/4}}} = {{{1/2}}}
Multiply by 20 to clear the denominators
20*{{{((2x+3))/5}}} - 20*{{{((x-2))/4}}} = 20*{{{1/2}}}
Cancel and you have:
4(2x+3) - 5(x-2) = 10
8x + 12 - 5x + 10 = 10
8x - 5x + 22 = 10
3x = 10 - 22
3x = -12
x = {{{(-12)/3}}}
x = -4
:
:
Let's see if this works, replace x with -4 in the original equation
{{{((2x+3))/5}}} - {{{((x-2))/4}}} = {{{1/2}}}
{{{((2(-4)+3))/5}}} - {{{((-4-2))/4}}} = {{{1/2}}}
{{{((-8+3))/5}}} - {{{((-6))/4}}} = {{{1/2}}}
{{{((-5))/5}}} - {{{((-6))/4}}} = {{{1/2}}}
-1 - ({{{-3/2}}}) = {{{1/2}}}
-1 + {{{3/2}}} = {{{1/2}}}
{{{-2/2}}} + {{{3/2}}} = {{{1/2}}}; we can say x=-4 does work