We are asked to write and graph a compound inequality that represents the numbers that are not solutions to the inequality from the given graph. This means that we are looking at the non-shaded region in the number line.
Let's start by graphing the inequality that represents the non-shaded area from the above number line. In order to do so, we will replace any closed points with open points. Likewise, we will replace any open points with closed points.
The red shaded area consists of all numbers that are greater than - 3 andless than or equal to 2.
-3< x and x ≤ 2
We can rewrite this compound inequality by noticing that x is between -3 and 2.
-3 < x ≤ 2
We obtained that each number greater than - 3 andless than or equal to 2 is not a solution to the inequality represented by the given graph.
