Question

graph the inequality
4 > x
which of the following graphs represents the inequality?
a.
b.
c.
d.
e.
f.

Explanation:

Step1: Analyze the inequality

The inequality is \(4 > x\), which can be rewritten as \(x < 4\). This means \(x\) can take any value less than 4, but not including 4 (since it's a strict inequality, \(>\) not \(\geq\)).

Step2: Analyze the number line graphs

• For a strict inequality (\(<\) or \(>\)), we use an open circle at the boundary point (4 in this case) to indicate that 4 is not included in the solution set.
• The arrow should point to the left of 4 (since we want values less than 4).

Looking at the options:

• Option A: Has an open circle at 4 and the arrow points to the left (towards values less than 4), which matches \(x < 4\).
• Option B: Has a closed circle at 3, which is not related to our boundary at 4.
• Option C: Has a closed circle at 4, but our inequality is strict (\(x < 4\), not \(x \leq 4\)), so a closed circle is incorrect.
• Option D: Arrow points to the right (values greater than 4), which is the opposite of what we need.
• Option E: Open circle at 3, not related to 4.
• Option F: Closed circle at 4 and arrow to the right, incorrect for \(x < 4\).

Answer:

A. The graph with an open circle at 4 and an arrow pointing to the left (towards values less than 4)