The problem asks to graphically represent the solutions for the inequality $-\frac{2}{3}x > 20$.

1. Problem Description

The problem asks to graphically represent the solutions for the inequality $-\frac{2}{3}x > 20$.

2. Solution Steps

To solve the inequality $-\frac{2}{3}x > 20$, we need to isolate $x$.

First, multiply both sides of the inequality by 3:

$3 \cdot (-\frac{2}{3}x) > 3 \cdot 20$

$-2x > 60$

Next, divide both sides of the inequality by -

2. Remember to flip the inequality sign when dividing by a negative number.

$\frac{-2x}{-2} < \frac{60}{-2}$

$x < -30$

To graphically represent the solutions $x < -30$, we can draw a number line. Place an open circle at -30 to indicate that -30 is not included in the solution. Then, shade the region to the left of -30, indicating that all values less than -30 are solutions to the inequality.

3. Final Answer

The solution to the inequality is $x < -30$.

The graphical representation would be a number line with an open circle at -30 and the line shaded to the left.