To solve the inequality -1/2x ≥ 17, we can start by isolating x on one side of the inequality.
Multiplying both sides by -2 (and reversing the direction of the inequality since we are multiplying by a negative number), we get:
x ≤ -34
So the solution to the inequality is x ≤ -34.
To graph the solution, we can draw a number line and mark -34 on it. Then we shade all the values of x that are less than or equal to -34. This can be represented by a closed circle at -34 and a shaded line to the left of -34, indicating that any value of x in that range satisfies the inequality.
Here is a graph of the solution:
```
<=====(●)-----------------------
-34
```
The shaded part of the line represents the values of x that satisfy the inequality -1/2x ≥ 17, and the closed circle at -34 indicates that x can be equal to -34 (since the inequality is "greater than or equal to").