Question

Ashley and Liam both have playlists on their music apps.
The number of playlists on Ashley’s app can be represented by X.
The number of playlists on Liam’s app is 4 times the number of playlists on Ashley’s app.
The total number of playlists on both their apps is at least 45.
What is the solution set for x, representing the number of playlists on Ashley’s app?

Answer 1

Olivia visited a stationery shop to buy journals.
She had $36 allocated for the purchase.
Olivia bought 4 journals.
Following the purchase, Olivia had less than $12 remaining.
What is the solution set for x, representing the cost of each journal?

Answer 2

Preston solved the inequality and graphed it on the number line. Which of the following is the inequality that he solved?
Number line:
<---------------------------------------------------------------->
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
The line goes from 10 to in between 1 and 2, its a closed circle.

Answer 3

1. 2.1x + 5.6 ≥ 8.75
2. 0.9x + 2.8 ≤ 5.95
3. 5.6x - 18.9 ≤ 0.7
4. 3.4x - 1.2 ≥ 4.75

Answer 4

Let's denote the number of playlists on Ashley's app as x.
The number of playlists on Liam's app is 4 times the number of playlists on Ashley’s app, so it is 4x.

The total number of playlists on both apps is at least 45, so we can write the equation:
x + 4x ≥ 45

Combining like terms, we get 5x ≥ 45.

Dividing both sides of the inequality by 5:
x ≥ 9

So the solution set for x, representing the number of playlists on Ashley’s app, is x ≥ 9.

Answer 5

Let's denote the cost of each journal as x.

Olivia bought 4 journals, so the total cost of the journals is 4x.

Olivia had $36 allocated for the purchase and had less than $12 remaining, so we can write the inequality:
36 - 4x < 12

Subtracting 36 from both sides:
-4x < 12 - 36

Simplifying:
-4x < -24

Dividing both sides of the inequality by -4 and reversing the inequality sign (since we are dividing by a negative number):
x > 6

So the solution set for x, representing the cost of each journal, is x > 6.

Answer 6

Based on the description and the number line provided, the inequality that Preston solved is:
x ≤ 2

Answer 7

The inequality that Preston solved is number 1: 2.1x + 5.6 ≥ 8.75.