Answer:
Step-by-step explanation:
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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
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _✍️
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⟹ \frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{3} )⟹
3
1
x−4=x−(
2
1
+
3
x
)
⟹ \frac{x}{3} - 4 = x - ( \frac{3 + 2x}{6} )⟹
3
x
−4=x−(
6
3+2x
)
⟹ \frac{x - 12}{3} = x - ( \frac{2x + 3}{6} )⟹
3
x−12
=x−(
6
2x+3
)
⟹ \frac{x - 12}{3} = x - \frac{2x - 3}{6}⟹
3
x−12
=x−
6
2x−3
⟹ \frac{x - 12}{3} = \frac{6x - 2x - 3}{6}⟹
3
x−12
=
6
6x−2x−3
⟹ \frac{x - 12}{3} = \frac{4x - 3}{6}⟹
3
x−12
=
6
4x−3
cancelling 6( R.H.S) By 3 From L.H.S
⟹ \frac{x - 12}{1} = \frac{4x - 3}{2}⟹
1
x−12
=
2
4x−3
⟹ 2(x - 12) = 4x - 3⟹2(x−12)=4x−3
⟹ 2x - 24 = 4x - 3⟹2x−24=4x−3
⟹ - 24 + 3 = 4x - 2x⟹−24+3=4x−2x
⟹ - 21 = 2x⟹−21=2x
⟹ x = - \frac{21}{2}⟹x=−
2
21
CHECK:-
⟹ \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
)
⟹ - \frac{21}{6} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{21}{6} )⟹−
6
21
−4=−
2
21
−(
2
1
−
6
21
)
⟹ - \frac{7}{2} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{7}{2} )⟹−
2
7
−4=−
2
21
−(
2
1
−
2
7
)
⟹ \frac{ - 7 - 8}{2} = - \frac{21}{2} - ( - \frac{6}{2} )⟹
2
−7−8
=−
2
21
−(−
2
6
)
⟹ - \frac{15}{2} = - \frac{21}{2} - ( - 3)⟹−
2
15
=−
2
21
−(−3)
⟹ - \frac{15}{2} = - \frac{21}{2} + 3⟹−
2
15
=−
2
21
+3
⟹ - \frac{15}{2} = \frac{ - 21 + 6}{2} = - \frac{15}{2}⟹−
2
15
=
2
−21+6
=−
2
15
THEREFORE,L.H.S=R.H.S
VERIFIED✔️
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HOPE IT HELPS YOU..
