The way to handle an inequality is to think of it as an equation first, plot the
line, and then figure out which side of the line to shade. This inequality is
extra complicated because of the absolute value. When you graph an
equation with absolute value, you generally get a line with a sharp bend, as in
all of the answer choices above. To find the graph of an absolute value
equation, figure out where that bend is. In this case |x + 2| has a turning-point
value of 0 when x + 2 = 0, which happens when x = −2. So the bend is at the
point (−2, 0). That narrows the choices down to (A) and (E).
Next, figure out which side gets shaded. Pick a convenient point on either side
and see if that point’s coordinates fit the given inequality. The point (0, 0) is an
easy one to work with. Do those coordinates satisfy the inequality?
The point (0, 0) must be on the shaded side of the bent line. The answer is (E).