Answer: C
Step-by-step explanation:
We are asked to find the solution to the compound inequality pictured on a number line. To do this, we will first solve each inequality for x.
[tex]\displaystyle -\frac{x}{2} \geq -2[/tex]
[tex]\displaystyle -3x < -15[/tex]
Multiply both sides of the first by -2 and flip the sign, divide both sides of the second by -3 and flip the sign.
[tex]\displaystyle x \leq 4[/tex]
[tex]\displaystyle x > 5[/tex]
Now, we can graph these two inequalities. One will be a filled-in circle to the left of 4, and one will be an open circle to the right of 5. This is shown by option C.
