Question

Solve the following linear equation and check the result :
x-1/4 + x-2/3 =25/6
Please explain me​

Answer 1

$\sf\dfrac{x-1}{4}$ + $\sf\dfrac{x-2}{3}$ = $\sf\dfrac{25}{6}$

Take LCM to denominators in LHS

LCM of 4, 3 is 12

$\sf\dfrac{3(x-1) + 4(x-2)}{12}$=$\sf\dfrac{25}{6}$

$\sf\dfrac{3x-3+4x-8}{12}$=$\sf\dfrac{25}{6}$

$\sf\dfrac{7x-11}{2}$=25

Do cross multiplication

7x -11 = 25(2)

7x -11 = 50

Tranpose -11 to rhs

7x = 50+11

7x = 61

x = $\sf\dfrac{61}{7}$

Know more :-

Transportations :-

If we transpose + after transpose it becomes -

If we tranpose - after tranpose it becomes +

If we tranpose × after tranpose it becomes ÷

If we tranpose ÷ after tranpose it becomes ×

Multiplication of signs

(+) ( -) = -

(-) ( +) = -

( + ) ( + ) = +

(-) (-) = +

Answer 2

Question:

prove that x-1/4 + x-2/3 =25/6

Answer :

x-1/4 + x - 2/3 =25/6

LCM of denominators :

then, we get

3(x-1)+4(x-2)/12 = 25/6

=>3x-3 +4x-8/12 = 25/6

=> 7x-11/12 = 25/6

=>7x-11= 25/6 ×12

=> 7x-11= 25×2

=> 7x-11=50

=> 7x=50+11

=> 7x=61

=> x=61/7

Answer :

61/7