Question 694367
{{{abs((4x-2)/5)=abs((6x+3)/2)}}}
The expressions inside the absolute value could be equal,
or one could equal the other times {{{(-1)}}}.
 
If they are equal:
{{{(4x-2)/5=(6x+3)/2}}} --> {{{2(4x-2)=5(6x+3)}}} (multiplying both sides of the equal sign times 10, or equating the cross-products)
{{{2(4x-2)=5(6x+3)}}} --> {{{8x-4=30x+15}}}
{{{8x-4=30x+15}}} --> {{{8x-4-8x-15=30x+15-8x-15}}} --> {{{-19=22x}}} --> {{{-19/22=22x/22}}} --> {{{highlight(x=-19/22)}}}
 
If one expression equals the other times {{{(-1)}}}:
{{{(-1)(4x-2)/5=(6x+3)/2}}} --> {{{(-1)(2)(4x-2)=5(6x+3)}}} (multiplying both sides of the equal sign times 10, or equating the cross-products)
{{{(-1)(2)(4x-2)=5(6x+3)}}} --> 
{{{-8x+4=30x+15}}} --> {{{-8x+4+8x-15=30x+15+8x-15}}} --> {{{-11=38x}}} --> {{{-11/38=38x/38}}} --> {{{highlight(x=-11/38)}}}