$\frac{x-1}{2}+\frac{2 x-1}{4}=\frac{x-1}{3}-\frac{2 x-1}{6}$.

Given: Expression: $\frac{x-1}{2}+\frac{2 x-1}{4}=\frac{x-1}{3}-\frac{2 x-1}{6}$.

To do: To solve the given expression $\frac{x-1}{2}+\frac{2 x-1}{4}=\frac{x-1}{3}-\frac{2 x-1}{6}$.

Solution: 

$\frac{x-1}{2}+\frac{2 x-1}{4}=\frac{x-1}{3}-\frac{2 x-1}{6}$

$\Rightarrow \frac{x-1}{2}-\frac{x-1}{3}=-\frac{2x-1}{6}-\frac{2x-1}{4}$

$\Rightarrow \frac{3( x-1)-2( x-1)}{6}=-( \frac{2( 2x-1)+3( 2x-1)}{12})$
 

$\Rightarrow \frac{3x-3-2x+2}{6}=-( \frac{4x-2+6x-3}{12})$

$\Rightarrow \frac{x-1}{6}=-\frac{10x-5}{12}$

$\Rightarrow 12( x-1)=-6( 10x-5)$

$\Rightarrow 12x-12=-60x+30$

$\Rightarrow 12x+60x=30+12$

$\Rightarrow 72x=42$

$\Rightarrow x=\frac{42}{72}$

$\Rightarrow x=\frac{7}{12}$

Thus, $x=\frac{7}{12}$$.

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Updated on: 10-Oct-2022

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