The equation given is:
[tex]\frac{2}{3}(6x+12)=-24[/tex]Solving for x:
[tex]\begin{gathered} \frac{2}{3}(6x+12)=-24 \\ 4x+8=-24 \\ 4x=-24-8 \\ 4x=-32 \\ x=-8 \end{gathered}[/tex]Now, let's solve all the equations and see which one(s) have a solution x = -8.
-- 4x +8 = - 24
4x = -32
x = -8
YES!
-- 9x+18 = - 24
9x = -42
x = -42/9
x = -14/3
No!
-- 4x = - 16
x = -4
No!
--
[tex]\begin{gathered} \frac{18x+36}{2}=-24 \\ 9x+18=-24 \\ 9x=-42 \\ x=-\frac{42}{9} \\ x=-\frac{14}{3} \end{gathered}[/tex]No!
-- 4x = -32
x = -32/4
x = -8
Yes!
Answer[tex]\begin{gathered} 4x+8=-24 \\ \text{and} \\ 4x=-32 \end{gathered}[/tex]