Question

last year, shannon and her friends walked a total of 13.5 miles in the school walk - a - thon. this year, their goal is to walk at least as many miles as they did last year. let d represent the distance, in miles, that shannon and her friends want to walk this year. which inequality models the story? $d > 13.5$ $d \geq 13.5$ $d < 13.5$ $d \leq 13.5$ graph the inequality that models the story. to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it. \

$$\begin{array}{ccccccccccc} \\leftarrow & \\vert & \\vert & \\vert & \\vert & \\vert & \\vert & \\vert & \\vert & \\vert & \ ightarrow \\\\ & 10 & 10.5 & 11 & 11.5 & 12 & 12.5 & 13 & 13.5 & 14 & 14.5 & 15 \\end{array}$$

Explanation:

Step1: Analyze the problem

The problem states that this year their goal is to walk at least as many miles as last year. Last year they walked 13.5 miles. "At least" means the distance \( d \) can be equal to 13.5 or more than 13.5.

Step2: Determine the inequality

The inequality that represents "at least" is \( d\geq13.5 \) because \( \geq \) means greater than or equal to.

Step3: Graph the inequality

For the inequality \( d\geq13.5 \), we start by finding the point 13.5 on the number line. Since the inequality is "greater than or equal to", we use a closed dot (because 13.5 is included in the solution set) at 13.5 and then draw an arrow to the right (because we want all values greater than or equal to 13.5).

Answer:

The inequality is \( d\geq13.5 \). For the graph, plot a closed dot at 13.5 and draw an arrow to the right.