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Please help me and answer

Please help me and answer-example-1
User Beeholder
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1 Answer

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Answer: Choice D

4 > |x+1| + 2

======================================================

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.

User Amr Ali
by
8.2k points

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