Question

katie wants to collect over 100 seashells. she already has 34 seashells in her collection. each day, she finds 12 more seashells on the beach. katie can use fractions of days to find seashells. write an inequality to determine the number of days, d, it will take katie to collect over 100 seashells. graph the solution set to this inequality. youre almost there there are still more parts of this question give it another try!

Explanation:

Step1: Set up the inequality

Katie already has 34 seashells and finds 12 seashells per day \(d\). She wants to collect over 100 seashells. So the inequality is \(34 + 12d>100\).

Step2: Solve the inequality

Subtract 34 from both sides: \(12d>100 - 34\), which simplifies to \(12d>66\).
Divide both sides by 12: \(d>\frac{66}{12}\), and \(\frac{66}{12}=5.5\), so \(d > 5.5\).

Step3: Graph the inequality

Since \(d>5.5\), on the number - line, we make an open circle at \(d = 5.5\) (because \(d = 5.5\) is not included in the solution set, as the inequality is \(d>5.5\)) and shade to the right of \(5.5\).

Answer:

The inequality is \(34 + 12d>100\). For graphing, make an open circle at \(5.5\) on the number - line and shade to the right.