Question

5x/3-(x - 1)/4=(x-3)/5 also verify the Answer .LHS=RHS​

Answer 1

★Given :-

$\sf \dfrac{5x}{3}-\dfrac{x-1}{4}=\dfrac{x-3}{5}$

★To find :-

The value of x and verify the answer

Solution :-

$\sf \dfrac{5x}{3}-\dfrac{x-1}{4}= \dfrac{x-3}{5}\\ \\ :\implies\sf \dfrac{(5x\times 4)- 3(x-1)}{12}= \dfrac{x-3}{5}\\ \\ :\implies\sf \dfrac{20x-3x+3}{12}= \dfrac{x-3}{5}\\ \\ \sf \ cross \ multiplication\\ \\ :\implies \sf 5(17x+3)= 12(x-3)\\ \\:\implies\sf 85x+15= 12x-36\\ \\ :\implies\sf 85x-12x= -36-15\\ \\ :\implies\sf 73x= -51\\ \\ :\implies\sf x=\dfrac{-51}{73}$

$\underline{\boxed{\sf\ \ x= \dfrac{-51}{73}}}$

VERIFICATION :-

★ First solve the half equation then put the value of x

$\sf \dfrac{5x}{3}-\dfrac{x-1}{4}= \dfrac{x-3}{5}\\ \\ :\implies\sf \dfrac{(5x\times 4)- 3(x-1)}{12}= \dfrac{x-3}{5}\\ \\ :\implies\sf \dfrac{20x-3x+3}{12}= \dfrac{x-3}{5}\\ \\ \sf \ cross \ multiplication\\ \\ :\implies \sf 5(17x+3)= 12(x-3)\\ \\ :\implies\sf 85x+15= 12x-36\\ \\ \sf \ put \ the \ value \ of \ x= \dfrac{-51}{94}\\ \\ :\implies \sf \bigg(\dfrac{85\times -51}{73}+15\bigg)= \bigg(\dfrac{12\times -51}{73}-36\bigg)\\ \\ :\implies\sf \bigg(\dfrac{-4335+1095}{73}\bigg)= \bigg(\dfrac{-612-2628}{73}\bigg)\\ \\ :\implies\sf \bigg(\dfrac{-3240}{73}\bigg)= \bigg(\dfrac{-3240}{73}\bigg)\\ \\ \sf \ \ L.H.S = R.H.S \ (hence \ verified \ !)$

$\underline{\boxed{\sf\ \ x= \dfrac{-51}{73}}}$

Answer 2

QueStI0N -

Solve the following Equation -

$\sf{ \dfrac{5x}{3} - \dfrac{ (x-1) }{ 4 } = \dfrac{(x - 3) }{ 5 } }$

Solution -

${ \dfrac{5x}{3} - \dfrac{ (x-1) }{ 4 } = \dfrac{(x - 3) }{ 5 } } \\ \\ \sf{ \dfrac{20x - 3( x- 1)}{12}} = \dfrac{(x - 3) }{ 5 } \\ \\ \sf{ \dfrac{20x - 3x + 3}{12} =\dfrac{(x - 3) }{ 5 } } \\ \\ \sf{ \dfrac{17x + 3}{12}} = \dfrac{(x - 3) }{ 5 } \\ \\ \sf { \bold{Cross \: Multiplying \: - }} \\ \\ \sf{ 12(x - 3) = 5(17x + 3) } \\ \\ \sf{ \leadsto{12x - 36 = 85x + 15}} \\ \\ \sf{ \mapsto{73x = - 51}} \\ \\ \sf{ \leadsto \: x \: = \: \dfrac{ - 51}{73}}$