Question

depending on the day of the week, a local gas station charges greater than $25 and up to $55 for a full tank of gas. these charges can be represented by the compound inequality 25 < w ≤ 55. which graph represents the charges? four number line graphs with 20,25,30,35,40,45,50,55,60, arrows, and circles/dots at 25 and 55 are shown

Explanation:

Step1: Analyze the inequality \(25 < w \leq 55\)

For \(25 < w\), this means \(w\) is greater than 25, so on the number line, there should be an open circle at 25 (since 25 is not included) and the line should go to the right from 25.
For \(w \leq 55\), this means \(w\) is less than or equal to 55, so on the number line, there should be a closed circle at 55 (since 55 is included) and the line should go to the left from 55.

Step2: Match with the graphs

• The first graph: Open circle at 25, closed circle at 55, and the line between them. This matches \(25 < w \leq 55\).
• The second graph: Closed circle at 25 (wrong, since \(w>25\) not \(w\geq25\)) and open circle at 55 (wrong, since \(w\leq55\) not \(w < 55\)).
• The third graph: Open circle at 25 and open circle at 55 (wrong, since 55 should be included).
• The fourth graph: Closed circle at 25 and closed circle at 55 (wrong, since 25 should not be included).

Answer:

The first graph (with open circle at 25 and closed circle at 55, and the line connecting them)