Answer: Choice C
The solution is [tex]z \ge 8[/tex]
The graph has an closed filled in circle at 8 on the number line, with shading to the right of that closed circle.
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Explanation:
[tex]-4z \le -32[/tex]
[tex]\frac{-4z}{-4} \ge \frac{-32}{-4}[/tex] see note below
[tex]z \ge 8[/tex]
note: I divided both sides by -4 to undo the multiplication done to z; the inequality sign flips because we divided both sides by a negative number
So the solution set is the set of z values such that z is 8 or larger. We are including the endpoint 8 so we use a filled in closed circle (not an open circle or hole). We include the endpoint because of the "or equal to" as part of ht inequality sign.
