a)
\(\eqalign{
& {x \over 3} - {{2x + 1} \over 2} = {x \over 6} - x \cr
& \Leftrightarrow {{2x} \over 6} - {{3.\left( {2x + 1} \right)} \over 6} = {x \over 6} - {{6x} \over 6} \cr
& \Leftrightarrow 2x-3\left( {2x + 1} \right) = x-6x \cr
& \matrix{
{ \Leftrightarrow 2x - 6x-3 = - 5x} \hfill \cr
{ \Leftrightarrow - 4x + 5x = 3} \hfill \cr
{ \Leftrightarrow x = 3} \hfill \cr} \cr} \)
Phương trình có nghiệm \(x = 3\).
b)
\(\eqalign{& {{2 + x} \over 5} - 0,5x = {{1 - 2x} \over 4} + 0,25 \cr
& \Leftrightarrow {{2 + x} \over 5} - {1 \over 2}x = {{1 - 2x} \over 4} + {{25} \over {100}} \cr
& \Leftrightarrow {{4\left( {2 + x} \right)} \over {20}} - {{10x} \over {20}} = {{5\left( {1 - 2x} \right)} \over {20}} + {5 \over {20}} \cr & \Leftrightarrow 4\left( {2 + x} \right)-10x = 5\left( {1-2x} \right) + 5 \cr
& \matrix{{ \Leftrightarrow 8 + 4x-10x = 5-10x + 5} \hfill \cr
{ \Leftrightarrow 4x-10x+10x = 5+5-8} \hfill \cr
{ \Leftrightarrow 4x = 10 - 8} \hfill \cr
\matrix{\Leftrightarrow 4x = 2 \hfill \cr
\Leftrightarrow x =\dfrac{2}{4} \hfill \cr} \hfill \cr} \cr & \Leftrightarrow x = {1 \over 2} \cr} \)
Vậy phương trình có nghiệm \(x = \dfrac{1 }{ 2}\)
