Question

Q:-solve and verify the equation
$\frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{ 3} )$


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Answer 1

$\red{\bold{\underline{\underline{QUESTION:-}}}}$

Q:-solve and verify the equation

$\frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{ 3} )$

$\huge\mathcal{Answer}$

$⟹\bold{</p><p> \frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{3} )}$

$⟹\bold{</p><p> \frac{x}{3} - 4 = x - ( \frac{3 + 2x}{6} )}$

$⟹\bold{</p><p> \frac{x - 12}{3} = x - ( \frac{2x + 3}{6} )}$

$⟹\bold{</p><p> \frac{x - 12}{3} = x - \frac{2x - 3}{6} }$

$⟹\bold{</p><p> \frac{x - 12}{3} = \frac{6x - 2x - 3}{6}}$

$⟹\bold{</p><p> \frac{x - 12}{3} = \frac{4x - 3}{6}}$

$\bold{\red{cancelling 6( R.H.S) By 3 From L.H.S}}$

$⟹ \bold{\frac{x - 12}{1} = \frac{4x - 3}{2} }</p><p>$

$⟹\bold{</p><p>2(x - 12) = 4x - 3}$

$⟹\bold{</p><p>2x - 24 = 4x - 3}$

$⟹\bold{</p><p> - 24 + 3 = 4x - 2x}$

$⟹\bold{</p><p> - 21 = 2x}$

$⟹\bold{</p><p>x = - \frac{21}{2} }$

$\bold{\red{CHECK:-}}$

$⟹ \bold{\frac{ - \frac{21}{2} }{3} - 4 = - \frac{21}{2} - ( \frac{1}{2} + ( - ) \frac{ \frac{21}{2} }{3} )}</p><p>$

$⟹\bold{</p><p> - \frac{21}{6} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{21}{6} )}$

$⟹\bold{</p><p> - \frac{7}{2} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{7}{2} )}$

$⟹\bold{</p><p> \frac{ - 7 - 8}{2} = - \frac{21}{2} - ( - \frac{6}{2} )}$

$⟹ \bold{- \frac{15}{2} = - \frac{21}{2} - ( - 3) }</p><p>$

$⟹\bold{</p><p> - \frac{15}{2} = - \frac{21}{2} + 3}$

$⟹\bold{</p><p> - \frac{15}{2} = \frac{ - 21 + 6}{2} = - \frac{15}{2}}$

THEREFORE,L.H.S=R.H.S

VERIFIED✓

HOPE IT HELPS YOU..

_____________________

Thankyou:)

Answer 2

$\LARGE{\underline{\sf \red{GIVEN:-}}}$

$\huge \bull \: \huge \sf{\frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{ 3} )}$

$\LARGE{\underline{\sf \red{TO \: FIND:-}}}$

• Solve and verify the equation.

$\LARGE{\underline{\sf \red{SOLUTION:-}}}$

$\boxed{\huge {\tt{\frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{ 3} )}}}$

$:\large\implies\tt\gray{ \dfrac{x}{3} - 4 = x - ( \dfrac{3 + 2x}{6}) }$

$:\large\implies \tt\gray{ \dfrac{x}{3} - 4 = x - \dfrac{ 3 + 2x}{6} }$

$:\large\implies \tt\gray{ \dfrac{x - 12}{3} = \dfrac{6x - 3 - 2x}{6} }$

$:\large\implies \tt\gray{ \dfrac{x - 12}{3} = \dfrac{4x - 3}{6} }$

Now let's apply the cross multiplication rule:-

$:\large\implies \tt\gray{6(x - 12) = 3(4x - 3)}$

$:\large\implies \tt\gray{6x - 72 = 12x - 9}$

$:\large\implies \tt\gray{6x - 12x = 72 - 9}$

$:\large\implies \tt\gray{ - 6x = 63}$

$:\large\implies \tt\gray{x = \cancel\dfrac{ - 63}{6} }$

$:\large\implies \boxed {\underline{ \tt\pink{x = - (\dfrac {21}{2}) }}}$

Now let's verify our result using LHS = RHS rule:-

$\huge\tt \color{teal}{ \frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{ 3} ) }$

$:\large\implies \tt \color{teal}{ \dfrac{1}{3} \times \dfrac{ - 21}{2} - 4 = - \dfrac{21}{2} - ( \dfrac{1}{2} + \dfrac{ \dfrac{ - 21}{2} }{3} )}$

$:\large\implies \tt \color{teal}{ \dfrac{ - 21}{6} - 4 = - \frac{21}{2} - ( \dfrac{1}{2} - \frac{ 21}{6}) }$

$:\large\implies \tt \color{teal}{ \dfrac{ - 21 - 24}{6} = - \dfrac{21}{2} - ( \dfrac{3 - 21}{6}) }$

$:\large\implies \tt \color{teal}{ \dfrac{ -45}{6} = - \dfrac{21}{2} + \dfrac{18}{6} }$

$:\large\implies \tt \color{teal}{ \dfrac{ - 45}{6} = \dfrac{ - 63 + 18}{6} }$

$:\large\implies \tt \color{red}{ \dfrac{ - 45}{6} = \dfrac{ - 45}{6} }$

$\huge{ \underline{ \overline{ \bf \orange{LHS=RHS}}}}$

$\large{ \underline{ \bf \green{Hence~Verified \huge \sf\dag}}}$