Question

Solve each of the following equations.
$\frac{1}{6} (1 - x) + \frac{2}{3} x - \frac{1}{4} (1 - 7x) = \frac{13}{6}$
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Answer 1

$\underline{\underline{\huge{\frak{\red{SoluTion}}}}}$

$\rightarrowtail\sf{\frac{1}{6}(1-x)+\frac{2}{3}x \;-\frac{1}{4}(1-7x)=\frac{13}{6}}$

$\rightarrowtail\sf{\frac{(1-x)}{6}+\frac{2x}{3}-\frac{(1-7x)}{4}=\frac{13}{6}}$

$\blue{\tt{taking\:LCM\:in\:LHS}}$

$\rightarrowtail\sf{\frac{2(1-x)+4(2x)-3(1-7x)}{12}=\frac{13}{6}}$

$\rightarrowtail\sf{\frac{2-2x+8x-3+21x}{12}=\frac{13}{6}}$

$\rightarrowtail\sf{27 x - 1 = \frac{13}{6}\times 12}$

$\rightarrowtail\sf{27 x - 1 = 26}$

$\rightarrowtail\sf{27 x = 27}$

$\implies\boxed{\pink{\bf{x = 1}}}$