Question

graph the inequality 4b > 125. four number lines with options and an i dont know yet option

Explanation:

Step1: Solve the inequality

To solve \(4b > 125\), we divide both sides by 4. So \(b > \frac{125}{4}=31.25\).

Step2: Analyze the number line graphs

• The inequality is \(b > 31.25\), so the graph should have an open circle (since it's \(>\), not \(\geq\)) at a value greater than 31.25 (30 is 30, which is less than 31.25; 31.25 is between 30 and 35, but we need an open circle and the line going to the right for values greater than 31.25).
• Looking at the options, the second graph (the one with the open circle at 30? Wait, no, wait: Wait, \(\frac{125}{4} = 31.25\), so the critical point is 31.25. Wait, maybe I misread the graphs. Wait, the second graph (the middle - ish one) has an open circle? Wait, no, let's re - check. Wait, the inequality is \(4b>125\), so \(b > 31.25\). So the graph should have an open circle (because the inequality is strict, \(>\)) and the arrow pointing to the right (for values greater than 31.25). Among the given graphs, the second graph (the one with the open circle and the arrow going to the right, starting from a point where the circle is at 30? Wait, no, maybe the labels are different. Wait, the second graph (the one in the middle of the first three) has an open circle? Wait, no, let's look at the x - axis: 0,5,10,15,20,25,30,35,40,... So 31.25 is between 30 and 35. The second graph (the one with the open circle at 30? No, wait, the second graph (the one where the line is blue and the circle is open? Wait, no, the correct graph should have an open circle (since \(b>31.25\), not \(b\geq31.25\)) and the line extending to the right (for values greater than 31.25). The second graph (the one with the open circle at 30? Wait, no, maybe I made a mistake. Wait, let's recalculate: \(125\div4 = 31.25\). So the solution is all real numbers greater than 31.25. So on the number line, we need an open circle (because it's a strict inequality) at a point greater than 31.25? Wait, no, 31.25 is the boundary. So the open circle should be at 31.25, but since the number line has marks at 30,35, etc., the closest is 30? No, wait, maybe the graphs are labeled differently. Wait, the second graph (the one with the open circle and the arrow going to the right, starting from 30? No, wait, the second graph (the middle of the first three) has an open circle? Wait, no, the second graph (the one where the line is blue and the circle is open) – wait, maybe the correct graph is the second one (the one with the open circle and the arrow pointing to the right, as the solution is \(b > 31.25\), so we need to show all values greater than 31.25, so the graph with the open circle (since it's not inclusive) and the arrow to the right.

Answer:

The second graph (the one with the open circle and the arrow pointing to the right, among the first three graphs)