Question

which shows the graph of $x < \frac{1}{3}$? \
a) blue arrow from below 0 (open or closed?) up to -2 \
b) blue arrow from below 0 (open or closed?) up to -2 \
c) blue arrow from below 0 (closed) down to 2 \
d) blue arrow from below 0 (open) down to 2

Explanation:

Step1: Analyze the inequality

The inequality is \( x < \frac{1}{3} \). For a number line graph of an inequality with a strict less - than sign (\(<\)), we use an open circle at the boundary point (since \(x\) cannot be equal to \(\frac{1}{3}\)) and the arrow should point to the left (because we want all values of \(x\) that are less than \(\frac{1}{3}\)).

Step2: Analyze each option

• Option A: It has a closed circle, which is used for inequalities with \(\leq\) or \(\geq\). Since our inequality is \(x < \frac{1}{3}\) (strict inequality), a closed circle is incorrect.
• Option B: It has an open circle (correct for \(<\)) and the arrow points to the left (indicating values less than the boundary point \(\frac{1}{3}\)). Let's check the other options to be sure.
• Option C: It has a closed circle, which is incorrect for a strict inequality \(x < \frac{1}{3}\).
• Option D: The arrow direction is to the right, which would represent \(x>\) some value, not \(x < \frac{1}{3}\). So this is incorrect.

Answer:

B) The graph with an open circle at \(\frac{1}{3}\) (or the appropriate position on the number line) and the arrow pointing to the left.