x ≤ 1 OR x ≥ 5
Explanation:
From the graph, we have 2 seperate arrows. Each indicating an inequality
For the arrow by the left:
The circle is shaded and it starts at 1 and extends towards the negative side of the axis.
Since its direcrion is towards the negative side, the inequality will beless than
The inequality < will have an equal sign attached because of the shaded circle.
x ≤ 1
For the arrow by the right:
Circle is shaded meaning an equal sign will be attached to the inequality
The shaded circle starts at 5 and extends towards the positive axis.
Since it extends towards the right side of x, the inequality will be greater than
x ≥ 5
Combining both inqualities:
we will be using OR to join the two inequalities together as both inequalities represents a union.
x ≤ 1 OR x ≥ 5
Hence, a compound inequality that describes the graph shown:
x ≤ 1 OR x ≥ 5
