Final answer:
The correct answer is C) Translate y = |x| up 4 units and shade inside the V, as this describes the translation of the V-shaped graph of y = |x| vertically upward by 4 units in the coordinate system and shading the region where y is greater than or equal to this new position.
Step-by-step explanation:
The inequality y ≥ |x| + 4 represents the set of points in the coordinate system where y is greater than or equal to the absolute value of x increased by 4 units. To graph this inequality, you would start with the graph of y = |x|, which is a V-shaped graph with the point of the V located at the origin (0, 0). According to the inequality, you would translate this V up 4 units vertically. This shifts the point of the V from the origin to (0, 4). To satisfy the inequality, you would then shade the area above the V including the boundary, which consists of all the points where y is greater than or equal to the value of |x| + 4.
The correct description from the options given is therefore C) Translate y = |x| up 4 units and shade inside the V.