The given inequality is:
[tex]-\frac{2}{3}x+2<-4[/tex]
Subtract 2 from both sides
[tex]\begin{gathered} -\frac{2}{3}x+2-2<-4-2 \\ -\frac{2}{3}x<-6 \end{gathered}[/tex]
Multiply both sides by 3
[tex]\begin{gathered} 3(-\frac{2}{3}x)<3(-6) \\ -2x<-18 \end{gathered}[/tex]
Divide both sides by 2
[tex]\begin{gathered} -\frac{2x}{2}<-\frac{18}{2} \\ -x<-9 \end{gathered}[/tex]
Multiply both sides by -1, and change the < symbol to >
[tex]\begin{gathered} -1(-x)>-1(-9) \\ x>9 \end{gathered}[/tex]
The solution to the given inequality is:
x > 9
The graph of the solution x > 9 is shown below
