ANSWER and EXPLANATION
We have the inequality:
[tex]\begin{gathered} \frac{4}{9}x\text{ }-\text{ 10 > }\frac{x}{3}\text{ -12} \\ \text{Collect like terms:} \\ \frac{4}{9}x\text{ - }\frac{x}{3}\text{ > -12 + 10} \\ \frac{1}{9}x\text{ > -2} \\ \text{Multiply both sides 9:} \\ x\text{ > -2 }\cdot\text{ 9} \\ x\text{ > -18} \end{gathered}[/tex]
Now, to draw that on the number line, we use an unshaded circle and the arrow will point to the right hand side:
