Answer: Choice D
4 > |x+1| + 2
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Step-by-step explanation:
Choice A can be ruled out because the result of any absolute value is never negative.
This means |x+1| cannot be smaller than -3.
In other words: -3 > |x+1| has no solutions
Similarly, choice B also leads to "no solutions" because we subtract 2 from both sides to get -1 > |x+2|. Therefore, we rule out choice B as well.
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Choice C can be solved through these steps
2 < |x+3| - 2
2+2 < |x+3|
4 < |x+3|
|x+3| > 4
x+3 > 4 or x+3 < -4
x > 4-3 or x < -4-3
x > 1 or x < -7
x < -1 or x > 1
The graph of this will have open holes at -7 and 1. Then you shade to the left of -7 and to the right of 1. This does not match the graph given to us.
We'll rule out choice C.
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Choice D can be solved through these steps
4 > |x+1| + 2
4-2 > |x+1|
2 > |x+1|
|x+1| < 2
-2 < x+1 < 2
-2-1 < x < 2-1
-3 < x < 1
The graph will have open holes at -3 and 1, with shading in between. This matches perfectly with the given graph.
This is why choice D is the answer.