Question

$\frac{x -4 }{3} = \frac{2x + 1}{6} + \frac{5x - 1}{2}$
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Answer 1

$\underline{\underline{\sf{\maltese\:\:Question}}}$

$\sf{Find\:the\:value\:of\:x\::\:\dfrac{x-4}{3}=\dfrac{2\:x+1}{6}+\dfrac{5\:x-1}{2}}$

$\underline{\underline{\sf{\maltese\:\:Given}}}$

$\sf{{\dfrac{x-4}{3}=\dfrac{2\:x+1}{6}+\dfrac{5\:x-1}{2}}$

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}\sf{\:\::Value\:\:of\:\:x}$

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

$\bf{x=-\dfrac{2}{5}}$

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

$\sf{{\dfrac{x-4}{3}=\dfrac{2\:x+1}{6}+\dfrac{5\:x-1}{2}}$

$\bullet\:\:\tt{Find\:\:the\:\:L.C.M\:\:(Least\:\:Common\:\:Multiplier)\:of\:3\:,\:6\:,\:2:}$

$\large{ \begin{array}{c|c} \tt 2 & \sf{ 3 , 6 , 2} \\ \cline{1-2} \tt 3 & \sf { 3 , 3 , 1} \\ \cline{1-2} & \sf{ 1 , 1 , 1} \end{array}}$    

$\tt{L.C.M\:\:(Least\:\:Common\:\:Multiplier)\:of\:3\:,\:6\:,\:2 =\:2\times 3= \underline{\underline{6}}}$

$\bullet\:\:\sf{{Multiply\:\:\dfrac{x-4}{3}=\dfrac{2\:x+1}{6}+\dfrac{5\:x-1}{2}\:\:by\:\:L.C.M}$

$\sf{\displaystyle\frac{x-4}{3}\times \:6=\frac{2x+1}{6}\times \:6+\frac{5x-1}{2}\times \:6}$

$\implies\sf{\displaystyle \frac{\left(x-4\right)\cdot \:6}{3}=\frac{2x+1}{6}\cdot \:6+\frac{5x-1}{2}\cdot \:6}$

$\implies\sf{\displaystyle 2\left(x-4\right)=\frac{2x+1}{6}\cdot \:6+\frac{5x-1}{2}\cdot \:6}$

$\implies\sf{2\left(x-4\right)=2x+1+3\left(5x-1\right)}$

$\implies\sf{2x-8=17x-2}$

$\implies\sf{2x-8+8=17x-2+8}$

$\implies\sf{2x=17x+6}$

$\implies\sf{2x-17x=17x+6-17x}$

$\implies\sf{-15x=6}$

$\implies\sf{\dfrac{-15x}{-15}=\dfrac{6}{-15}}$

$\implies\bf{x=-\dfrac{2}{5}}$

Answer 2

$\sf{Answer}$

★ Step by step explanation:-

Given:-

$\sf\dfrac{x-4}{3}$ = $\sf\dfrac{2x+1}{6}$+$\sf\dfrac{5x-1}{2}$

Take LCM To the denominator of RHS

$\sf\dfrac{x-4}{3}$ = $\sf\dfrac{2x+1+3(5x-1}{6}$

$\sf\dfrac{x-4}{3}$ =$\sf\dfrac{2x+1+15x-3}{6}$

$\sf\dfrac{x-4}{3}$ = $\sf\dfrac{17x-2}{6}$

$\sf{x-4}$ = $\sf\dfrac{17x-2}{2}$

Do cross multiplication

$\sf{2(x-4)}$ = $\sf{17x-2}$

$\sf{2x-8}$ = $\sf{17x-2}$

Transpose like terms to a side

$\sf{2x-17x=8-2}$

$\sf{-15x=6}$

Make a subject x

$\sf\dfrac{-6}{15}$ = x

Simplify value of x

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

So the value of x is -3/5

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