Step-by-step explanation:
\huge\mathfrak\green{\bold{\underline{β{ βΙ§Ξ΅ΕΟΙ±Ξ΅ΕΰΈ¨Ι}β}}}
ββΙ§Ξ΅ΕΟΙ±Ξ΅ΕΰΈ¨Ιβ
\red{\bold{\underline{\underline{QUESTION:-
QUESTION:β
Q:-solve and verify the equation
\frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{ 3} )
3
1
xβ4=xβ(
2
1
+
3
x
)
\huge\tt\underline\blue{Answer }
Answer
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _βοΈ
ββββββββββXXXβββββββββββββ
βΉ \frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{3} )βΉ
3
1
xβ4=xβ(
2
1
+
3
x
)
βΉ \frac{x}{3} - 4 = x - ( \frac{3 + 2x}{6} )βΉ
3
x
β4=xβ(
6
3+2x
)
βΉ \frac{x - 12}{3} = x - ( \frac{2x + 3}{6} )βΉ
3
xβ12
=xβ(
6
2x+3
)
βΉ \frac{x - 12}{3} = x - \frac{2x - 3}{6}βΉ
3
xβ12
=xβ
6
2xβ3
βΉ \frac{x - 12}{3} = \frac{6x - 2x - 3}{6}βΉ
3
xβ12
=
6
6xβ2xβ3
βΉ \frac{x - 12}{3} = \frac{4x - 3}{6}βΉ
3
xβ12
=
6
4xβ3
cancelling 6( R.H.S) By 3 From L.H.S
βΉ \frac{x - 12}{1} = \frac{4x - 3}{2}βΉ
1
xβ12
=
2
4xβ3
βΉ 2(x - 12) = 4x - 3βΉ2(xβ12)=4xβ3
βΉ 2x - 24 = 4x - 3βΉ2xβ24=4xβ3
βΉ - 24 + 3 = 4x - 2xβΉβ24+3=4xβ2x
βΉ - 21 = 2xβΉβ21=2x
βΉ x = - \frac{21}{2}βΉx=β
2
21
CHECK:-
βΉ \frac{ - \frac{21}{2} }{3} - 4 = - \frac{21}{2} - ( \frac{1}{2} + ( - ) \frac{ \frac{21}{2} }{3} )βΉ
3
β
2
21
β4=β
2
21
β(
2
1
+(β)
3
2
21
)
βΉ - \frac{21}{6} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{21}{6} )βΉβ
6
21
β4=β
2
21
β(
2
1
β
6
21
)
βΉ - \frac{7}{2} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{7}{2} )βΉβ
2
7
β4=β
2
21
β(
2
1
β
2
7
)
βΉ \frac{ - 7 - 8}{2} = - \frac{21}{2} - ( - \frac{6}{2} )βΉ
2
β7β8
=β
2
21
β(β
2
6
)
βΉ - \frac{15}{2} = - \frac{21}{2} - ( - 3)βΉβ
2
15
=β
2
21
β(β3)
βΉ - \frac{15}{2} = - \frac{21}{2} + 3βΉβ
2
15
=β
2
21
+3
βΉ - \frac{15}{2} = \frac{ - 21 + 6}{2} = - \frac{15}{2}βΉβ
2
15
=
2
β21+6
=β
2
15
THEREFORE,L.H.S=R.H.S
VERIFIEDβοΈ
ββββββββββXXXβββββββββββββ
HOPE IT HELPS YOU..
