Answer:
Answer Option 3
Explanation:
If you look at the vertical line at x = 2 we see that everything to the left of the line is a ≤ relationship since it is a solid line
So this inequality is of the form
x ≤ 2
We can eliminate answer choices 2 and 4 which has y≤ 2
That leaves only the first and third choices
Since the other two bounding lines of the shaded region are dotted lines, both of these represent a < or > inequality
Let's analyze answer choice 1, second inequality
y > x + 2
Choose a point well within the shaded region and see if that point satisfies this inequality
A great point will be (0, 0) which makes computation easier
Does (0, 0) satisfy the second inequality?
Is y = 0 > 0 + 2 ?
Is 0 > 2?
False
So the first answer choice is out leaving the correct answer choice as answer choice #3
Just to be on the safe side let us analyze all three inequalities of the third answer choice using (0, 0)
x ≤ 2? ===> 0 ≤ 2? True
y < x + 2? ==> 0 < 0 + 2 ==> 0 < 2? True
y > (- 1/4)x - 3? ==> 0 > -1/4 · 0 - 3? ==> 0 > -3 True
Hence double-checked option 3 as verified