Question

What is the graph of the absolute value inequality?|x + 5| ≥ y – 2

Answer 1

Best way to describe the answer is that the point will touch -6 and the left top corner will be shaded in

Answer 2

Step-by-step explanation:

|x + 5| ≥ y – 2

First we replace the inequality sign by = sign

|x + 5| = y – 2

solve for y and then graph it

add 2 on both sides

y = |x + 5|+ 2

Equation is in the form of y=a|x-h|+k

where (h,k) is the vertex

h = -5  and k = 2

So vertex is (-5,2)

Now make a table

x            y = |x + 5|+ 2

-10         y = |-10+5| + 2= 7

-5            y = |-5+5| + 2= 2

0              y = |0+5| + 2= 7

Now plot all the points we got the table and graph it

Now we do shading

Lets pick any point inside the V shaped graph and check with our inequality

LEts pick (-5,5)

|x+5| ≥ y – 2

plug in -5 for x  and 5 for y

|-5+5| ≥ 5– 2

0 > = 3, its false

So we cannot shade the part containing (-5,5)

we shade the bottom part on graph

the graph is attached below