Question

1/3(2x-1)-1/4((2x+1) =1/12(2-x)

Answer 1

$\frac{1}{3} (2x - 1) - \frac{1}{4}(2x + 1) = \frac{1}{12} (2 - x) \\ \\ ( \frac{2x - 1}{3} ) - ( \frac{2x + 1}{4} ) = ( \frac{2 - x}{12} ) \\ \\ for \: \: making \: the \: denominators \\ \: equal : \\ \\ multiply \: 1st \: bracket \\ (both \: numerator \: and \: denominator) \: \\ by \: 4 \\ \\ and \: multiply \: 2nd \: bracket \\ (both \: numerator \: and \: denomintor) \\ \: by \: 3 \: \\ \\ 4( \frac{2x - 1}{3} ) - 3( \frac{2x + 1}{4} ) = ( \frac{2 - x}{12} ) \\ \\ \frac{8x - 4}{12} - \frac{6x - 3}{12} = \frac{2 - x}{12} \\ \\ \frac{8x - 4 - 6x + 3}{12} = \frac{2 - x}{12} \\ \\ due \: to \: same \: denominator \\ \: 12 \: gets \: cancelled : \\ \\ 8x - 4 - 6x + 3 = 2 - x \\ \\ 8x - 6x - 4 + 3 = 2 - x \\ \\ 2x - 1 = 2 - x \\ \\ 2x + x = 2 + 1 \\ \\ 3x = 3 \\ \\ x = \frac{3}{3} \\ \\ x = 1$