Question 696803
Given : {{{((a-x)/(a-b))-2=(c-x)/(b-c)}}}

Solution:
{{{((a-x)- 2(a-b))/ (a-b)=(c-x)/(b-c)}}}
{{{ (a-x-2a+2b)*(b-c) = (c-x)(a-b)}}}
{{{ (2b-a-x)(b-c) = ac-ax-bc+bx}}}
{{{ 2b^2-ab-bx-2bc+ac+cx = ac-ax-bc+bx}}}
Taking out the common factors from both sides  : ac

{{{ 2b^2-ab-bx-2bc+cx+ax+bc-bx = 0}}}
{{{2b^2-2bx+ax+cx-ab-bc = 0}}}
{{{2b^2+x(a+c-2b) = ab+bc}}}
{{{x(a+c-2b)= ab+bc-2b^2}}}
{{{x(a+c-2b)= b(a+c-2b)}}}
{{{x = b}}}