Find the value of "K"
[tex] \frac{-2}{3} ( \frac{1}{2} + k) = \frac{-55}{39} [/tex]
[tex]\frac{-2}{3}*\frac{1}{2} + \frac{-2}{3}*k = \frac{-55}{39} [/tex]
[tex]\frac{-2}{6} + \frac{-2k}{3} = \frac{-55}{39}[/tex]
least common multiple (6,3,39) = 78
[tex]\frac{-26}{\diagup\!\!\!\!\!78} + \frac{-52k}{\diagup\!\!\!\!\!78} = \frac{-110}{\diagup\!\!\!\!\!78}[/tex]
[tex]- 26 - 52k = - 110[/tex]
[tex]- 52k = - 110 + 26[/tex]
[tex]- 52k = - 84\:simplify\:by\:*(-1)[/tex]
[tex]52k = 84[/tex]
[tex]k = \frac{84}{52}\: \frac{\div4}{\div4} \to \boxed{\boxed{k = \frac{21}{13} }}\end{array}}\qquad\quad\checkmark[/tex]
