Question

which of the following shows the graph of the inequality ( i > -\frac{3}{4} )?
a) graph with open circle at -3/4 (between -1 and -1/2) and arrow to the right

b) graph with closed circle at -3/4 and arrow to the left

c) graph with open circle at -3/4 and arrow to the left

d) graph with closed circle at -3/4 and arrow to the right

Explanation:

Step1: Analyze the inequality

The inequality is \( i > -\frac{3}{4} \). First, we need to understand the position of \( -\frac{3}{4} \) on the number line. \( -\frac{3}{4}=-0.75 \), which is between -1 and 0 (closer to 0). The inequality is "greater than", so the graph should have an open circle (since \( i \) is not equal to \( -\frac{3}{4} \)) and the arrow pointing to the right (towards larger numbers).

Step2: Evaluate each option

• Option A: Open circle at a point, but the arrow is pointing left (towards smaller numbers), which is for \( i < \) some value. Eliminate A.
• Option B: Closed circle (which would be for \( i \geq \) or \( i \leq \)) and arrow pointing left. Eliminate B.
• Option C: Open circle (correct for \( > \)) and arrow pointing right (towards larger numbers, which is correct for \( i > -\frac{3}{4} \)). Let's check the position: The marked point should be at \( -\frac{3}{4} \approx -0.75 \), which is between -1 and 0. The open circle and right arrow match.
• Option D: Closed circle and arrow pointing right. But the inequality is \( > \), not \( \geq \), so closed circle is incorrect. Eliminate D.

Answer:

C) (the option with open circle at \( -\frac{3}{4} \) (or the position between -1 and 0) and arrow pointing to the right)