Graph the solution if the this inequality 4/9x-10> x/3-12

You want to isolate the x-term from the constant term, so you can subtract x/3 and add 10. This gives you

... 4/9x -10 -x/3 +10 > x/3 -12 -x/3 +10

... 1/9x > -2 . . . . . . collect terms

Now, you can multiply by 9 to see the condition on x.

... 9(1/9x) > -2(9)

... x > -18

On the x-y plane, the graph of this will be a dashed line at x=-18, and the half-plane to the right of that line will be shaded.

On a number line, there will be an open circle at x=-18, and the number line to the right of that circle will be marked (bold, colored, shaded, whatever).