The graph that represents the inequality |x + 1| + 2 < –1 is at option 1. Since the equation has no solution (empty set), the graph does not get intersected.
What is the inequality equation?
The inequality equation is the one that is true for some values of the variable. The inequalities may be greater than, less than, greater than or equal, or less than or equal.
Solving the given inequality:
The given inequality equation is
|x + 1| + 2 < –1
⇒ |x + 1| +2 - 2 < –1 -2
⇒ |x + 1| < –3
So, (x+1) < -3 or (x+1) > -3
⇒ x < -4 or x > -4
This is not possible. So the solution set of the given inequality is empty.
So, the graph is shown for different expressions.
The expressions are considered as
f(x) = |x + 1| + 2 and y < -1
In option 1, the graph shows these two expressions. So, the correct representation for the given inequality is option 1.
Since there is no solution, they do not have any intersecting points in the graph.
Learn more about inequalities here:
https://brainly.com/question/9774970
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