Question

$\frac{x + 2}{6} - ( \frac{11 - x}{3} - \frac{1}{4} ) = \frac{3x - 4}{12}$
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Answer 1

${ \huge☆{ \underline {\underline {\tt {Answer}}}}☆}$

$\large \sf\frac{x + 2}{6} - ( \frac{11 - x}{3} - \frac{1}{4} ) = \frac{3x - 4}{12}$

Take L.C.M. to make the denominators same.

L.C.M. of 3 and 4=12

$\sf \implies \frac{11 - x}{3} \times \frac{4}{4} = \frac{44 - 4x}{12} \\ \\ \sf \implies \frac{1}{4} \times \frac{3}{3} = \frac{3}{12} \\ \\ \\ \implies \sf \frac{x + 2}{6} - \frac{44 - 4x - 3}{12} = \frac{3x - 4}{12} \\ \\ \implies \sf \frac{x + 2}{6} - \frac{41 - 4x}{12} = \frac{3x - 4}{12} \\ \\ \implies \sf \frac{x + 2}{6} = \frac{3x - 4}{12} + \frac{41 - 4x}{12} \\ \\ \implies \sf \frac{x + 2}{6} = 1x + 37 \\ \\ \implies \sf \cancel x + 2 - \cancel x = 37 \times 6 \\ \\ \implies 2 = 15416 \\ \\ \implies \frac{15416}{2} = 7708$

Answer 2

$\Huge\mathfrak\purple{answer:}$

$\sf{ }$

$\bf \frac{x + 2}{6} - \bigg( \frac{11 - x}{3} - \frac{1}{4} \bigg) = \frac{3x - 4}{12} \\ \\ \bf » - \longrightarrow \frac{x + 2}{6} - \bigg( \frac{4(11 - x) - 3}{12} \bigg) = \frac{3x - 4}{12} ~~~~~~~~\\ \\ \bf » - \longrightarrow \frac{x + 2}{6} - \bigg( \frac{44 - 4x - 3}{12} \bigg) = \frac{3x - 4}{12} ~~~~~~~~~~~ \\ \\ \bf » - \longrightarrow \frac{x + 2}{6} - \frac{41 - 4x}{12} = \frac{3x - 4}{12} ~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \bf » - \longrightarrow \bigg( \frac{2(x + 2) - 41 - 4x}{12} \bigg) = \frac{3x - 4}{12} ~~~~~~~~~~~~~ \\ \\ \bf » - \longrightarrow \frac{2x + 4 - 41 - 4x}{12} = \frac{3x - 4}{12} ~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \bf » - \longrightarrow \frac{(2x - 4x) + (4 - 41)}{12} = \frac{3x - 4}{12} ~~~~~~~~~~~~~~~~ \\ \\ \bf » - \longrightarrow \frac{ - 2x - 37}{12} = \frac{3x - 4}{12} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \bf Cross \: multiplying \: we \: get : ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \bf \cancel{12}( - 2x - 37) = \cancel{12}(3x - 4)~~~~~~ \\ \bf » - \longrightarrow - 2x - 37 = 3x - 4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \bf » - \longrightarrow - 2x - 3x = - 4 + 37~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \bf » - \longrightarrow - 5x = 33 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\ \bf » - \longrightarrow x = \frac{33}{ - 5} = \purple{ \underline{ \underline{ \frac{ - 33}{5} }}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$