-2x>1/9 {xix_ _}

To solve the inequality -2x > 1/9, we need to isolate x.

Step 1: Multiply both sides of the inequality by -1 (or divide both sides by -2) to flip the inequality sign:
-2x > 1/9 [Multiplying by -1]
x < -1/18

So the solution to the inequality -2x > 1/9 is x < -1/18.

To represent the solution on a number line, you can draw a ray starting from -1/18 going towards the left side of the number line. Since the inequality is strict (x < -1/18), you would use an open circle at -1/18 to indicate that it is not included in the solution.

Below is a visual representation of the solution:

<=====o---------------------- (number line)
-1/18