Question

Carlotta subscribes to the Hot-Burn music service. She can download no more than 16 song files per week. Carlotta has already downloaded 13 song files this week. Write, solve, and graph an inequality to show how many more songs Carlotta can download.

Answer 1

Carlotta can download at most 3 more songs this week as she has a limit of 16 downloads and she has already downloaded 13. The inequality representing this situation is x ≤ 3. The graph includes all numbers to the left of and including point 3 on a number line.

Step-by-step explanation:

To figure out how many more songs Carlotta can download after already downloading 13 song files on the Hot-Burn music service, we write an inequality. Let x represent the number of songs Carlotta can still download this week. The inequality is:

x ≤ 16 - 13

This simplifies to:

x ≤ 3

Carlotta can download at most 3 more songs this week since she cannot exceed her limit of 16 total downloads.

Solving the inequality:

• x ≤ 3

The solution set consists of all numbers less than or equal to 3. To graph this inequality on a number line:

1. Draw a number line.
2. Mark the point corresponding to 3.
3. Shade the region to the left of this point (including the point) to represent all possible download amounts that are less than or equal to 3.