Question

please tell me answer ​

Answer 1

Answer :-

x = 1/12

Given :-

$\dfrac{x + 1}{2} + \dfrac{x + 2}{3} + \dfrac{x - 5}{4} = \dfrac{x}{12}$

To find :-

x value

SOLUTION  :-  

》 Take L.C.M to the denominator in L.H.S

》 L.C.M of 2, 3, 4 is 12

$\dfrac{6(x + 1) + 4(x + 2) + 3(x - 5)}{12} = \dfrac{x}{12}$

$\dfrac{6x + 6 + 4x + 8 + 3x - 15}{12} = \dfrac{x}{12}$

$6x + 6 + 4x + 8 + 3x - 15 = x$

》 Keeping  like terms together

$6x + 4x + 3x + 6 + 8 - 15 = x$

$13x - 1 = x$

$13x - x = 1$

$12x = 1$

$\red{x = \dfrac{1}{12} }$

So, the value of x is 1/12

Verification:-

Substitute value of x it should be L.H.S = R.H.S

$\dfrac{x + 1}{2} + \dfrac{x + 2}{3} + \dfrac{x - 5}{4} = \dfrac{x}{12}$

$\dfrac{ \dfrac{1}{12} + 1}{2} + \dfrac{ \dfrac{1}{12} + 2}{3} + \dfrac{ \dfrac{1}{12} - 5}{4} = \dfrac{ \dfrac{1}{12} }{12}$

$\dfrac{ \dfrac{1 + 12}{12} }{2} + \dfrac{ \dfrac{1 + 24}{12} }{3} + \dfrac{ \dfrac{1 - 60}{12} }{4} = \dfrac{1}{144 }$

$\dfrac{ \dfrac{13}{12} }{2} + \dfrac{ \dfrac{25}{12} }{3} + \dfrac{ \dfrac{ - 59}{12} }{4} = \dfrac{1}{144 }$

$\dfrac{13}{24} + \dfrac{25}{36} + \dfrac{ - 59}{48} = \dfrac{1}{144}$

Take L.C.M to the denominators in L.C.M

L.C.M of 24,36,48 is 144

$\dfrac{78 + 100 - 177}{144} = \dfrac{1}{144}$

$\dfrac{178- 177}{144} = \dfrac{1}{144}$

$\dfrac{1}{144} = \dfrac{1}{144}$

Hence verified !

Know more :-

Transportations :-

If we transpose + after transpose it becomes -

If we transpose - after transpose it becomes +

If we transpose × after transpose it becomes ÷

If we transpose ÷ after transpose it becomes ×

Multiplication of signs:-

(+) ( -) = -

(-) ( +) = -

( + ) ( + ) = +

(-) (-) = +

Answer 2

Answer :-

x = 1/12

Given :-

$\dfrac{x + 1}{2} + \dfrac{x + 2}{3} + \dfrac{x - 5}{4} = \dfrac{x}{12}$

To find :-

x value

SOLUTION  :-  

》 Take L.C.M to the denominator in L.H.S

》 L.C.M of 2, 3, 4 is 12

$\dfrac{6(x + 1) + 4(x + 2) + 3(x - 5)}{12} = \dfrac{x}{12}$

$\dfrac{6x + 6 + 4x + 8 + 3x - 15}{12} = \dfrac{x}{12}$

$6x + 6 + 4x + 8 + 3x - 15 = x$

》 Keeping  like terms together

$6x + 4x + 3x + 6 + 8 - 15 = x$

$13x - 1 = x$

$13x - x = 1$

$12x = 1$

$\red{x = \dfrac{1}{12} }$

So, the value of x is 1/12

Verification:-

Substitute value of x it should be L.H.S = R.H.S

$\dfrac{x + 1}{2} + \dfrac{x + 2}{3} + \dfrac{x - 5}{4} = \dfrac{x}{12}$

$\dfrac{ \dfrac{1}{12} + 1}{2} + \dfrac{ \dfrac{1}{12} + 2}{3} + \dfrac{ \dfrac{1}{12} - 5}{4} = \dfrac{ \dfrac{1}{12} }{12}$

$\dfrac{ \dfrac{1 + 12}{12} }{2} + \dfrac{ \dfrac{1 + 24}{12} }{3} + \dfrac{ \dfrac{1 - 60}{12} }{4} = \dfrac{1}{144 }$

$\dfrac{ \dfrac{13}{12} }{2} + \dfrac{ \dfrac{25}{12} }{3} + \dfrac{ \dfrac{ - 59}{12} }{4} = \dfrac{1}{144 }$

$\dfrac{13}{24} + \dfrac{25}{36} + \dfrac{ - 59}{48} = \dfrac{1}{144}$

Take L.C.M to the denominators in L.C.M

L.C.M of 24,36,48 is 144

$\dfrac{78 + 100 - 177}{144} = \dfrac{1}{144}$

$\dfrac{178- 177}{144} = \dfrac{1}{144}$

$\dfrac{1}{144} = \dfrac{1}{144}$

Hence verified !

Know more :-

Transportations :-

If we transpose + after transpose it becomes -

If we transpose - after transpose it becomes +

If we transpose × after transpose it becomes ÷

If we transpose ÷ after transpose it becomes ×

Multiplication of signs:-

(+) ( -) = -

(-) ( +) = -

( + ) ( + ) = +

(-) (-) = +