Question

d. $y \leq 3\frac{1}{3}$ (ex 2)
e. $0 > v$ (ex 2)
write an inequality for each graph.
f. (ex 3) number line with -1, 0, 1, 2, 3, open circle at 0.5?
g. (ex 3) number line with 8, 10, 12, 14, 16, closed diamond at 12
h. (ex 3) number line with 30, 40, 50, 60, open circle at 45?
i. (ex 3) number line with -1, 0, 1, closed diamond at 0.5?
j. (ex 4) chemistry the boiling point of a liquid is the temperature at which it changes into a gas. the boiling point of water under normal atmospheric conditions is $100^circ$c. write an inequality to represent the temperatures for which water is a gas. graph the solution set of the inequality.

Explanation:

Part f

Step 1: Identify the critical point and direction

The graph has an open circle at \( \frac{1}{2} \) (or 0.5) and the arrow points to the right. An open circle means the point is not included, so we use \( > \) or \( < \). Since the arrow is to the right (increasing values), we use \( > \). Let the variable be \( x \).

Step 2: Write the inequality

So the inequality is \( x > \frac{1}{2} \) (or \( x > 0.5 \)).

Step 1: Identify the critical point and type of circle

The graph has a closed circle at 12. A closed circle means the point is included, so we use \( \geq \) or \( \leq \). The arrow points to the right (increasing values), so we use \( \geq \). Let the variable be \( x \).

Step 2: Write the inequality

So the inequality is \( x \geq 12 \).

Step 1: Identify the critical point and direction

The graph has an open circle at 45 (since the marks are 30, 40, 45, 50, 60? Wait, the marks are 30, 40, then the open circle is at 45? Wait, the number line has 30, 40, then a mark at 45? Wait, the original graph: 30, 40, then the open circle, then 50, 60. So the critical point is 45? Wait, no, the distance between 30 and 40 is 10, so each mark is 5? Wait, 30, 35, 40, 45, 50, 60? Wait, the open circle is at 45? Wait, the problem's graph: "30 40 50 60" with an open circle between 40 and 50. So the critical point is 45? Wait, no, maybe each tick is 5? So 30, 35, 40, 45, 50, 60. The open circle is at 45? Wait, no, the open circle is between 40 and 50, so the critical value is 45? Wait, no, maybe the variable is \( x \), and the open circle is at 45? Wait, no, let's re - examine. The number line: 30, 40, then the open circle, then 50, 60. So the mid - point between 40 and 50 is 45. The arrow points to the left (decreasing values). An open circle means the point is not included, so we use \( < \) or \( > \). Since the arrow is to the left, we use \( < \). Let the variable be \( x \).

Step 2: Write the inequality

So the inequality is \( x < 45 \).

Answer:

\( x > \frac{1}{2} \)

Part g