Answer:
Third choice
x < -2; y ≤ -x -2
Step-by-step explanation:
The dotted vertical line passing through x = 2 shows it is a < inequality corresponding to x < -2. If it were a ≤ inequality, then it would be a solid vertical line
That eliminates the first two choices. Second choice is x < -3 which is not correct because we can see that the shaded region includes everything below x = -2 not below x = -3. For example, x = -2.5 is in the shaded region
So we have to choose between the third and fourth choices. Note that the line equation for choice 3 is y = -x -2 and for choice 4 it is y = -x +2
Choose (x, y) = (-3, 0)
choice 3
y ≤ -x -2
Substitute x with -3 in -x + 2 giving
-(-3) -2 = 3 - 2 = 1
Point(-3,1) lies on the line and therefore does satisfy the second inequality
choice 4
y ≤ -x + 2
Substitute x with -3 giving
-x + 2 = -(-3) + 2 = 3 + 2 =5
But (-3, 5) is not on the line. In fact, it is outside the shaded region so it does not satisfy the second inequality
So the correct choice is the third choice
x < -2, y ≤ -x -2
