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Explanation:
Solve each inequality for x
[tex]5x \ge 20[/tex] solves to [tex]x \ge 4[/tex] after dividing both sides by 5
[tex]x+14 < 16[/tex] solves to [tex]x < 2[/tex] after subtracting 14 from both sides
The original system solves to [tex]x \ge 4 \ \text{ or } \ x < 2[/tex] which is the same as [tex]x < 2 \ \text{ or } \ x \ge 4[/tex]
So x is either less than 2, equal to 4, or larger than 4.
The graph that fits the description above is Choice B. We have an open hole at x = 2 to show we don't include this value. In contrast, there's a filled in hole or closed circle at x = 4 to include this value. The blue shaded region is the set of all possible x values, so we shade to the left of x = 2 and to the right of x = 4.
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Side note: I don't know why your teacher thought it was a good idea to make the answer choice tiles be larger than the actual problem itself. It should be the other way around. Though to be fair, it's probably a design choice that your teacher wasn't involved in.
