Question

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

Answer 1

$\huge{\bold☘}\mathfrak\pink{\bold{\underline{{ ℘ɧεŋσɱεŋศɭ}}}}{\bold☘}$

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

Q:-solve and verify the equation

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

$\huge\tt\underline\blue{Answer }$

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _✍️

══════════XXX═════════════

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

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

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

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

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

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

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

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

$⟹\bold{</p><p>2(x - 12) = 4x - 3}$

$⟹\bold{</p><p>2x - 24 = 4x - 3}$

$⟹\bold{</p><p> - 24 + 3 = 4x - 2x}$

$⟹\bold{</p><p> - 21 = 2x}$

$⟹\bold{</p><p>x = - \frac{21}{2} }$

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

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

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

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

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

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

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

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

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

VERIFIED✔️

══════════XXX═════════════

HOPE IT HELPS YOU..

_____________________

Thankyou:)

Answer 2

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

QUESTION:−

Q:-solve and verify the equation

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

3

1

x−4=x−(

2

1

+

3

x

)

$\huge\tt\underline\blue{Answer }$

Answer

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _✍️

══════════XXX═════════════

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

3

1

x−4=x−(

2

1

+

3

x

)

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

3

x

−4=x−(

6

3+2x

)

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

3

x−12

=x−(

6

2x+3

)

⟹$\bold{ \frac{x - 12}{3} = x - \frac{2x - 3}{6} }$⟹

3

x−12

=x−

6

2x−3

⟹$\bold{ \frac{x - 12}{3} = \frac{6x - 2x - 3}{6}}$⟹

3

x−12

=

6

6x−2x−3

⟹$\bold{ \frac{x - 12}{3} = \frac{4x - 3}{6}}$⟹

3

x−12

=

6

4x−3

$\bold{\red{cancelling 6( R.H.S) By 3 From L.H.S}}$cancelling6(R.H.S)By3FromL.H.S

⟹ $\bold{\frac{x - 12}{1} = \frac{4x - 3}{2} }$⟹

1

x−12

=

2

4x−3

⟹$\bold{ 2(x - 12) = 4x - 3}$⟹2(x−12)=4x−3

⟹$\bold{ 2x - 24 = 4x - 3}$⟹2x−24=4x−3

⟹$\bold{ - 24 + 3 = 4x - 2x}$⟹−24+3=4x−2x

⟹$\bold{ - 21 = 2x}$⟹−21=2x

⟹$\bold{ x = - \frac{21}{2} }$⟹x=−

2

21

$\bold{\red{CHECK:-}}$CHECK:−

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

3

−

2

21

−4=−

2

21

−(

2

1

+(−)

3

2

21

)

⟹$\bold{ - \frac{21}{6} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{21}{6} )}$⟹−

6

21

−4=−

2

21

−(

2

1

−

6

21

)

⟹$\bold{ - \frac{7}{2} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{7}{2} )}$⟹−

2

7

−4=−

2

21

−(

2

1

−

2

7

)

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

2

−7−8

=−

2

21

−(−

2

6

)

⟹ $\bold{- \frac{15}{2} = - \frac{21}{2} - ( - 3) }$⟹−

2

15

=−

2

21

−(−3)

⟹$\bold{ - \frac{15}{2} = - \frac{21}{2} + 3}$⟹−

2

15

=−

2

21

+3

⟹[tex]\bold{ - \frac{15}{2} = \frac{ - 21 + 6}{2} = - \frac{15}{2}}[tex]⟹−

2

15

=

2

−21+6

=−

2

15

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

VERIFIED✔️

══════════XXX═════════════

HOPE IT HELPS YOU..

_____________________

Thankyou:)