Question

challenge you have a bag of x peanuts. you share these peanuts with 4 of your friends. each of you gets at least 35 peanuts. the inequality 35 ≤ x ÷ 5 models this situation. graph the solutions of this inequality. choose the correct graph below. a. graph with arrow from 0 through 175, 200 b. graph with arrow from 0 through 160, 175 open circle c. graph with arrow from 0 through 35, 40 d. graph with open circle at 7, arrow right e. graph with open circle at 175, arrow right f. graph with closed circle at 7, arrow right g. graph with open circle at 35, arrow right h. graph with closed circle at 175, arrow right

Explanation:

Step1: Solve the inequality

We start with the inequality \(35\leq\frac{x}{5}\). To solve for \(x\), we multiply both sides of the inequality by 5. When we multiply both sides of an inequality by a positive number, the direction of the inequality sign remains the same. So, \(35\times5\leq\frac{x}{5}\times5\), which simplifies to \(175\leq x\) or \(x\geq175\).

Step2: Analyze the number line graphs

We need to find the number line that represents \(x\geq175\). A closed circle (or a filled - in dot) at 175 (since the inequality is "greater than or equal to") and an arrow pointing to the right (because we want all values greater than or equal to 175). Looking at the options, we check the position of the circle and the direction of the arrow. The graph that has a closed (or appropriate) marking at 175 and the arrow going to the right (indicating all values greater than or equal to 175) is the one that represents the solution. From the given options, the graph that matches \(x\geq175\) is the one with the marking at 175 and the arrow to the right (for example, if we consider the options, the graph like option F or the one with the blue line starting at 175 and going right, but from the description, we can infer that the correct graph is the one where the solution is \(x\geq175\)).

Answer:

The correct graph is the one representing \(x\geq175\) (e.g., the graph with a closed or appropriate marking at 175 and an arrow to the right, such as the relevant option among A - H that shows \(x\geq175\)). If we assume the options are as per the visual, the correct option (e.g., F if it has the correct marking) or the one with the blue line starting at 175 and extending to the right. (Since the exact option labels are a bit unclear from the text, but based on the solution \(x\geq175\), the graph should have a marking at 175 and arrow right.)