Mathematics

The key is understanding what the inequality symbol tells you about whether the boundary point itself is included. Since $x \le -7$ uses "less than or equal to," the value $-7$ satisfies the inequality—it's part of the solution set. A closed circle marks points that are included; an open circle marks points that are excluded. So you need a closed circle at $x = -7$.

The key is understanding what the inequality symbol tells you about whether the boundary point itself is included. Since $x \le -7$ uses "less than or equal to," the value $-7$ satisfies the inequality—it's part of the solution set. A closed circle marks points that are included; an open circle marks points that are excluded. So you need a closed circle at $x = -7$.