Question

-2/3 (1/2 + k) =-55/39

Answer 1

Find the value of "K"

`(-2)/(3) ( (1)/(2) + k) = (-55)/(39)`

`(-2)/(3)*(1)/(2) + (-2)/(3)*k = (-55)/(39)`

`(-2)/(6) + (-2k)/(3) = (-55)/(39)`
least common multiple (6,3,39) = 78

`(-26)/(\diagup\!\!\!\!\!78) + (-52k)/(\diagup\!\!\!\!\!78) = (-110)/(\diagup\!\!\!\!\!78)`

`- 26 - 52k = - 110`

`- 52k = - 110 + 26`

`- 52k = - 84\:simplify\:by\:*(-1)`

`52k = 84`

`k = (84)/(52)\: (/4)/(/4) \to \boxed{\boxed{k = (21)/(13) }}\end{array}}\qquad\quad\checkmark`