Question

Solve: - ( 2/3 a - 1/3) + 5/3a = -4.Solve the equation.

3
4
(2a − 6) + 1
2
= 2
5
(3a + 20)

a =

Answer 1

To solve the equation for a, we first apply the distributive property to the left side:

`\begin{gathered} -\mleft((2)/(3)a-(1)/(3)\mright)+(5)/(3)a=-4 \\ -(2)/(3)a+(1)/(3)+(5)/(3)a=-4 \end{gathered}`

Now, we add similar terms on the left side of the equation:

`\begin{gathered} \text{ Reorder} \\ -(2)/(3)a+(5)/(3)a+(1)/(3)=-4 \\ \mleft(-(2)/(3)+(5)/(3)\mright)a+(1)/(3)=-4 \\ \mleft((-2+5)/(3)\mright)a+(1)/(3)=-4 \\ (3)/(3)a+(1)/(3)=-4 \\ 1\cdot a+(1)/(3)=-4 \\ a+(1)/(3)=-4 \end{gathered}`

Now, we subtract 1/3 from both sides of the equation:

`\begin{gathered} a+(1)/(3)-(1)/(3)=-4-(1)/(3) \\ a=-(4)/(1)-(1)/(3) \\ a=-(4\cdot3)/(1\cdot3)-(1)/(3) \\ a=-(12)/(3)-(1)/(3) \\ a=(-12-1)/(3) \\ \boldsymbol{a=-(13)/(3)} \end{gathered}`

Therefore, the value of a that satisfies the equation is -13/3.