Given inequality y<=|x+2| can be solved by graphing in two steps. First graph for y=|x+2| then shade it for the inequality sign <= to get final graph.
STEP1: Graph y=|x+2|
This is an absolute equation so compare y=|x+2| with standard equation
y=a|x-h|+k
we get a=1, h=-2, k=0
In that formula (h,k) gives vertex so that means vertex for y=|x+2| is at (-2,0)
x-coordinate of vertex is x=-2
We know that graph of absolute function is always in shape of letter V. so to get other sides we find one point on both sides of vertex.
Lets use x=-3 for left side point and x=0 for the right side point.
Plugging x=-3 into y=|x+2| gives y=|-3+2|=|-1|=1
so the left side point is (-3,1)
Plugging x=0 into y=|x+2| gives y=|0+2|=|2|=2
so the right side point is (0,2)
Now we graph all three points and join them by two lines starting from vertex (-2,0) to get graph A.
STEP2: Shading the graph for inequality.
To find the direction of shading we can plug any random point (except the points on obtained graph) in original inequality to check if that test point satisfies the inequality or not.
Let's use (0,0) as test point because that is not on the graph.
plug x=0, y=0 into y<=|x+2|
0<=|0+2|
0<=|2|
0<=2
Which is clearly TRUE.
True means shade in the direction of test point otherwise shade in opposite direction of test point.
We got TRUE result hence we will shade the graph in the region where point (0,0) lies
Hence final graph is B as attached below.
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For second question you can repeat exactly same process and get graph C.