To solve the equation for a, we first apply the distributive property to the left side:
[tex]\begin{gathered} -\mleft(\frac{2}{3}a-\frac{1}{3}\mright)+\frac{5}{3}a=-4 \\ -\frac{2}{3}a+\frac{1}{3}+\frac{5}{3}a=-4 \end{gathered}[/tex]Now, we add similar terms on the left side of the equation:
[tex]\begin{gathered} \text{ Reorder} \\ -\frac{2}{3}a+\frac{5}{3}a+\frac{1}{3}=-4 \\ \mleft(-\frac{2}{3}+\frac{5}{3}\mright)a+\frac{1}{3}=-4 \\ \mleft(\frac{-2+5}{3}\mright)a+\frac{1}{3}=-4 \\ \frac{3}{3}a+\frac{1}{3}=-4 \\ 1\cdot a+\frac{1}{3}=-4 \\ a+\frac{1}{3}=-4 \end{gathered}[/tex]Now, we subtract 1/3 from both sides of the equation:
[tex]\begin{gathered} a+\frac{1}{3}-\frac{1}{3}=-4-\frac{1}{3} \\ a=-\frac{4}{1}-\frac{1}{3} \\ a=-\frac{4\cdot3}{1\cdot3}-\frac{1}{3} \\ a=-\frac{12}{3}-\frac{1}{3} \\ a=\frac{-12-1}{3} \\ \boldsymbol{a=-\frac{13}{3}} \end{gathered}[/tex]Therefore, the value of a that satisfies the equation is -13/3.
