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Question: Write a system of linear inequalities that describes the shaded region.



A ) x ≥ -2 and x < 0
B ) x ≥ -2 and x > 0
C ) x ≤ -2 and x < 0
D ) x ≤ -2 and x > 0

Steps to derive

1 There are two lines that bound the shaded region.

2 So, the system must have two linear inequalities.

3 The first inequality is bounded by the vertical line that passes through the point (-2, 0).

4 Then the equation of this line is x = -2.

5 The shaded region is on and to right of the solid boundary line.

6 So, the first inequality is x ≥ -2.

7 The second inequality is bounded by the vertical line that passes through the point (0, 0).

8 Then the equation of this line is x = 0.

9 The shaded region is to the left of the dashed boundary line.

10 So, the second inequality is x < 0.

11 The system of inequalities that describes the shaded region is x ≥ -2 and x < 0.



Hence the right answer is Option A

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