Question

let x be the number of tickets elena sells.
10x ≥ 120
x ≥ 12
elena needs to sell at least 12 tickets.
decide whether elena can sell each number of tickets to reach her goal.
yes
no
12 tickets
13 tickets
13.5 tickets
which graph best represents the number of tickets elena can sell to reach her goal?
four number line graphs are shown below, with different markings and blue lines/ dots. the first has a solid dot at 12 and a blue line to 17. the second has solid dots at 12,13,14,15,16,17 and a blue line. the third has solid dots at 13,14,15,16,17 and a blue line. the fourth has an open dot at 12 and a blue line to 17.

Explanation:

Step1: Analyze the inequality

We have the inequality \(10x \geq 120\). To solve for \(x\), we divide both sides by 10: \(\frac{10x}{10} \geq \frac{120}{10}\), which simplifies to \(x \geq 12\). Also, since \(x\) represents the number of tickets, it should be a non - negative integer (we can't sell a fraction of a ticket in this context, but for the graph of the inequality \(x\geq12\) in the real number line, we consider real numbers first and then the context of tickets).

Step2: Analyze the graph features

• For an inequality of the form \(x\geq a\) (where \(a = 12\) here), the graph on the number line should have a closed circle at \(x = 12\) (because the inequality is "greater than or equal to") and the line should extend to the right (towards positive infinity) from \(x = 12\).
• Let's check each graph:
• The first graph: It has a closed circle at 12 and the line extends to the right. This matches the inequality \(x\geq12\).
• The second graph: It has dots at specific integer values (12, 13, 14, 15, 16, 17) which is more like representing the number of tickets as integers, but the inequality \(x\geq12\) in the context of real numbers (before considering the ticket - as - integer context) is a ray starting at 12 and going right. However, if we consider that \(x\) must be an integer (number of tickets), but the question is about the graph that best represents the number of tickets (and the inequality \(x\geq12\) where \(x\) is a real number representing the number of tickets, and in reality, tickets are integers, but the graph of the inequality \(x\geq12\) on the number line is a closed circle at 12 and a ray to the right). The first graph has a closed circle at 12 and the ray to the right, which is the standard way to represent \(x\geq12\) on the number line. The other graphs either have open circles (which is wrong for \(\geq\)) or represent discrete points which is not the standard way to represent the inequality \(x\geq12\) (the inequality is about a range of values, not just specific integers, although in the context of tickets, \(x\) is an integer, but the graph of the inequality \(x\geq12\) in the number line is a closed circle at 12 and a ray to the right).

Answer:

The first graph (the one with a closed circle at 12 and the line extending to the right from 12)