[tex] \frac{2}{3} (9 + x) = -5 (4 - x) \\ \\ \frac{2(9 + x)}{3} = -5(4 - x) \ / \ simplify \\ \\ 2(9 + x) = -15(4 - x) \ / \ multiply \ each \ sides \ by \ 3 \\ \\ 18+ 2x = -60 + 15x \ / \ expand \\ \\ 18 + 2x = 15x - 60 \ / \ regroup \ the \ terms \\ \\ 18 = 15x - 60 - 2x \ / \ subtract\ 2x \ from \ each \ side \\ \\ 18 = 13x - 60 \ / \ simplify \\ \\ 18 + 60 = 13x \ / \ add \ 60 \ to \ each \ side \\ \\ 78 = 13x \ / \ simplify \\ \\ \frac{78}{13} = x \ / \ divide \ each \ side \ by \ 13 \\ \\ [/tex]
[tex]6 = x \ / \ simplify \\ \\ x = 6 \ / \ switch \ the \ sides \\ \\ [/tex]
So, your answer to this problem is x = 6.
