Question

question
match the inequality below to the correct graph.
$2 < x$
a (graph with open circle at 2, arrow left), b (graph with closed circle at 2, arrow left), c (graph with closed circle at 2, arrow right), d (graph with open circle at 2, arrow right)

Explanation:

Step1: Analyze the inequality

The inequality is \(2 < x\), which can be rewritten as \(x > 2\). This means we are looking for all real numbers greater than 2.

Step2: Analyze the graph features

• For an inequality \(x > a\) (where \(a = 2\) here), the graph should have an open circle at \(a\) (because \(x\) is not equal to \(a\)) and an arrow pointing to the right (since we want values greater than \(a\)).

Step3: Evaluate each option

• Option A: The open circle is at a value less than 2 (around 2? Wait, no, looking at the number line, the open circle is at a position, but the arrow is to the left. So this represents \(x < \text{that number}\), not \(x > 2\). Eliminate A.
• Option B: There is a closed circle, which would represent \(x \leq \text{or} \geq\) that number, but we need an open circle for \(x > 2\). Also, the arrow is to the left, so it's for values less than or equal to that number. Eliminate B.
• Option C: There is a closed circle, which is incorrect for \(x > 2\) (we need open circle). Eliminate C.
• Option D: The open circle is at 2 (or the position corresponding to 2 on the number line) and the arrow is pointing to the right, which represents \(x > 2\). This matches our inequality.

Answer:

D