Answer: The solution is -5 < a < 1. The graph is attached below as an image.
Explanation:
Let x = |a+2|. So that means we can replace the entire "|a+2|" part with just "x"
We go from this: 4 + |a+2| < 7
to this: 4 + x < 7
That's the same as x+4 < 7
Solve for x by subtracting 4 from each side
x+4 < 7
x+4-4 < 7 - 4
x < 3
Now replace x with |a+2| to get |a+2| < 3
From here, we use the rule that |x| < k breaks down into -k < x < k for some positive number k. In this case, k = 3 and x = a+2
So..
|a+2| < 3
-3 < a+2 < 3 ... use the rule mentioned above
-3-2 < a+2-2 < 3-2 ... subtract 2 from all sides
-5 < a < 1
The solution for 'a' is the compound inequality -5 < a < 1 meaning that 'a' can be anything between -5 and 1. The value of 'a' cannot equal -5, nor can it equal 1.
To graph this, we draw out a number line. Then plot two open circles at -5 and 1. Shade between these open circles. Do not fill in the open circles. They are not filled in to tell the reader "do not include the value as part of the solution". Think of them as potholes in the road where you cannot drive.
Check out the attached image below for the graph.
