Question

solve the Linea Equation
3x-2/4+x=2/3- 2x+3/3​

Answer 1

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

• $\sf\:\frac{3x-2}{4} + x =\frac{2}{3}-\frac{2x+3}{3}$

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$\large\sf\underline{To\:find\::}$

• Value of x.

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

$\sf\:\frac{3x-2}{4} + x =\frac{2}{3}-\frac{2x+3}{3}$

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• LCM of 4 and 1 in LHS and that of 3 and 3 in RHS

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$\sf\implies\:\frac{3x-2+4x}{4} =\frac{2-(2x+3)}{3}$

$\sf\implies\:\frac{7x-2}{4} =\frac{2-2x-3}{3}$

$\sf\implies\:\frac{7x-2}{4} =\frac{-1-2x}{3}$

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• Cross multiplying

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$\sf\implies\:3(7x-2)=4(-1-2x)$

$\sf\implies\:21x-6=-4-8x$

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• Transposing (-8x) to the other side

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$\sf\implies\:21x+8x-6=-4$

$\sf\implies\:29x-6=-4$

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• Transposing (-6) to the other side

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$\sf\implies\:29x=-4+6$

$\sf\implies\:29x=2$

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• Transposing 29 to the other side

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$\large{\mathfrak\red{\implies\:x\:=\:\frac{2}{29}}}$

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_______________________

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$\large\sf\underline{Verifying\::}$

$\sf\:\frac{3x-2}{4} + x =\frac{2}{3}-\frac{2x+3}{3}$

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• Substituting the value of x as $\sf\:\frac{2}{29}$

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$\sf\implies\:\frac{3 \times \frac{2}{29} -2}{4} + \frac{2}{29} =\frac{2}{3}-\frac{2 \times \frac{2}{29} +3}{3}$

$\sf\implies\:\frac{\frac{6}{29} -2}{4} + \frac{2}{29} =\frac{2}{3}-\frac{\frac{4}{29} +3}{3}$

$\sf\implies\:\frac{\frac{6-58}{29}}{4} + \frac{2}{29} =\frac{2}{3}-\frac{\frac{4+87}{29}}{3}$

$\sf\implies\:\frac{\frac{-52}{29}}{4} + \frac{2}{29} =\frac{2}{3}-\frac{\frac{91}{29}}{3}$

$\sf\implies\:\frac{-52}{29} \times \frac{1}{4} + \frac{2}{29} =\frac{2}{3}-\frac{91}{29} \times \frac{1}{3}$

$\sf\implies\:\frac{-52}{116} + \frac{2}{29} =\frac{2}{3}-\frac{91}{87}$

$\sf\implies\:\frac{-52+8}{116} =\frac{58-91}{87}$

$\sf\implies\:\frac{-44}{116} =\frac{-33}{87}$

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• Cross multiplying

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$\sf\implies\:-44 \times 87 =-33 \times 116$

$\sf\implies\:\cancel{-}3828 =\cancel{-}3828$

$\sf\implies\:3828 =3828$

$\small\fbox\blue{Hence\:Verified}$

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$\dag\:\underline{\sf So\:the\:required\:value\:of\:x\:is\:\frac{2}{29}.}$

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!! Hope it helps !!