The graph that represents the solution set for the inequality 1/2 x≤18 is the third graph.
The inequality symbol: "≤" means "less than or equal to". This indicates that the solution set includes both numbers less than 18 and 18 itself.
Converting the inequality to an equality: To visualize the solution set on a number line, we can first rewrite the inequality as an equality. In this case, we can multiply both sides by 2 to get: x=36.
Marking the solution on the number line: On the number line in the image, locate the point 36. Since the inequality includes values less than or equal to 18, a closed circle should be used at 36.
Shading the appropriate side: Since the inequality specifies "less than or equal to", the side of the number line to the left of 36 (including 36 itself) should be shaded. This represents all the numbers that satisfy the inequality.
Therefore the graph that represents the solution set for the inequality 1/2 x≤18 is the third graph.