Question

I know the but I don't solution please send me right solution
the answer is -171/35​

Answer 1

$\large\underline{\sf{Solution-}}$

Given equation is

$\rm :\longmapsto\:\dfrac{3}{4}\bigg(\dfrac{7x - 1}{4} \bigg) - \bigg(2x - \dfrac{1 - x}{2} \bigg) = x + 11$

$\rm :\longmapsto\:\bigg(\dfrac{21x - 3}{16} \bigg) - \bigg(\dfrac{4x - (1 - x)}{2} \bigg) = x + 11$

$\rm :\longmapsto\:\bigg(\dfrac{21x - 3}{16} \bigg) - \bigg(\dfrac{4x - 1 + x}{2} \bigg) = x + 11$

$\rm :\longmapsto\:\bigg(\dfrac{21x - 3}{16} \bigg) - \bigg(\dfrac{5x - 1}{2} \bigg) = x + 11$

$\rm :\longmapsto\:\dfrac{21x - 3 - 8(5x - 1)}{16} = x + 11$

$\rm :\longmapsto\:\dfrac{21x - 3 - 40x + 8}{16} = x + 11$

$\rm :\longmapsto\:\dfrac{ - 19x + 5}{16} = x + 11$

$\rm :\longmapsto\: - 19x + 5 = 16x + 176$

$\rm :\longmapsto\: - 19x - 16x =176 - 5$

$\rm :\longmapsto\: - 35x = 171$

$\bf\implies \:x = \: - \: \dfrac{171}{35}$

Check :-

Consider RHS

$\rm :\longmapsto\:x + 11$

$\rm \: = \: \: - \dfrac{171}{35} + 11$

$\rm \: = \: \: \dfrac{ - 171 + 385}{35}$

$\rm \: = \: \: \dfrac{214}{35}$

Consider LHS

$\rm :\longmapsto\:\dfrac{3}{4}\bigg(\dfrac{7x - 1}{4} \bigg) - \bigg(2x - \dfrac{1 - x}{2} \bigg)$

$\rm \: = \: \: \:\dfrac{3}{4}\bigg(\dfrac{ \dfrac{ - 1197}{35} - 1}{4} \bigg) - \bigg( - \dfrac{342}{35} - \dfrac{1 + \dfrac{171}{35} }{2} \bigg)$

$\rm \: = \: \: \:\dfrac{3}{4}\bigg(\dfrac{ \dfrac{ - 1197 - 35}{35} }{4} \bigg) - \bigg( - \dfrac{342}{35} - \dfrac{ \dfrac{35 + 171}{35} }{2} \bigg)$

$\rm \: = \: \: \:\dfrac{3}{4}\bigg(\dfrac{ \dfrac{ - 1232}{35} }{4} \bigg) - \bigg( - \dfrac{342}{35} - \dfrac{ \dfrac{206}{35} }{2} \bigg)$

$\rm \: = \: \: - \dfrac{3}{4} \times \dfrac{308}{35} - \bigg( - \dfrac{342}{35} - \dfrac{103}{35} \bigg)$

$\rm \: = \: \: - \dfrac{231}{35} - \bigg(\dfrac{ - 342 - 103}{35} \bigg)$

$\rm \: = \: \: - \dfrac{231}{35} - \bigg(\dfrac{ - 445}{35} \bigg)$

$\rm \: = \: \: - \dfrac{231}{35} + \bigg(\dfrac{ 445}{35} \bigg)$

$\rm \: = \: \: \dfrac{214}{35}$

Hence, LHS = RHS

Thus, Verified