1 . Kyle has $4 more than twice as much money as Lana. Lana has x dollars. Kyle does not have enough money to buy a video game that costs $56, but he has enough money to buy a textbook that cost $38.

A. Write a compound inequality that represents all the possible amount of money that Kyle could have in terms of X. Show your work.

B. What is the LEAST amount of money Lana could have? Show your work.

( Continued ) Lana has a whole number of dollars.
C. List the different possible amounts of money, in dollars, Lana could have. Show your work.

2. Javier has a website on which he posts photos and videos. The day he started the website, he posted 12 photos and no videos. For each day after he started the website, he posts 4 new photos and one new video.

A. Complete the table below to show the total number of photos and the total number of videos that are on the website based on the number of days since Javier started the website. ( Graph is image attached. )

B. Write the rate of change in the total number of photos on the website each day since Javier started the website. Show all work.

C. Write a linear equation to show the relationship between the total number of videos (v) on the website and the number of days (x) since Javier started the website. Show all work.

A) 38≤2x+4<56

B) 17
C) (pick any of the following...)
-17,18,19,20,21,22

Kyle has 2x+4, so

38 <= 2x+4 < 56
34 <= 2x < 52
17 <= x < 26

for the photos, after x days he has 12+4x photos and x videos

A. To represent the possible amount of money Kyle could have in terms of x:

Let's say Lana has x dollars.
Twice as much money as Lana would be 2x dollars.
Kyle has $4 more than twice as much money as Lana, so he has 2x + 4 dollars.

Based on the given information, Kyle cannot afford a video game that costs $56, but he can afford a textbook that costs $38. This means that his money must be greater than or equal to $38 and less than $56.

Therefore, the compound inequality that represents all the possible amount of money that Kyle could have is:

38 ≤ 2x + 4 < 56

B. To find the least amount of money Lana could have:

Lana has a whole number of dollars, which means she cannot have a fractional or decimal value for x. Therefore, the minimum value for x would be 1.

Substituting x = 1 into the equation for Lana's money, we get:

Lana has 1 dollar.

So, the least amount of money Lana could have is $1.

C. To list the different possible amounts of money Lana could have:

Since Lana has a whole number of dollars, the possible values for x would be all positive integers.

Therefore, the different possible amounts of money Lana could have are:

x = 1: Lana has $1.
x = 2: Lana has $2.
x = 3: Lana has $3.
...
and so on.

The possible amounts of money Lana could have are all positive whole numbers.

2.

A. The table showing the total number of photos and videos on the website based on the number of days since Javier started the website is as follows:

Days | Total Photos | Total Videos
---------------------------------
0 | 12 | 0
1 | 16 | 1
2 | 20 | 2
3 | 24 | 3
4 | 28 | 4

B. The rate of change in the total number of photos on the website each day since Javier started the website is constant at 4 photos per day. This means that for each additional day, there are 4 more photos on the website.

C. The relationship between the total number of videos (v) on the website and the number of days (x) since Javier started the website can be represented by a linear equation.

Since Javier started with 0 videos and posts one new video each day, we can use the formula for a linear equation:

v = mx + b

Here, m represents the rate of change (which is 1 in this case) and b represents the initial value (which is 0 in this case). Therefore, the linear equation describing the relationship between the total number of videos (v) on the website and the number of days (x) since Javier started the website is:

v = 1x + 0

Simplifying, the equation becomes:

v = x

A. To represent all the possible amount of money that Kyle could have in terms of X, we can use a compound inequality.

Let's break down the given information:
- Kyle has $4 more than twice as much money as Lana.
- Lana has x dollars.
- Kyle does not have enough money to buy a video game that costs $56.
- Kyle has enough money to buy a textbook that costs $38.

Based on this information, we can write the compound inequality:
2x + 4 < 56 and 2x + 4 >= 38

Explanation:
- The first part of the compound inequality, "2x + 4 < 56," represents that Kyle doesn't have enough money to buy the video game that costs $56. This means that the total amount of money Kyle has (twice Lana's money plus $4) is less than $56.
- The second part of the compound inequality, "2x + 4 >= 38," represents that Kyle has enough money to buy the textbook that costs $38. This means that the total amount of money Kyle has (twice Lana's money plus $4) is greater than or equal to $38.

B. To find the least amount of money Lana could have, we need to substitute the value of x in the compound inequality.

Substituting x in the compound inequality:
2x + 4 >= 38

Now solve for x:
2x >= 34
x >= 17

So, the least amount of money Lana could have is $17.

C. To list the different possible amounts of money Lana could have, we need to consider the values greater than or equal to 17 since x >= 17.

Possible amounts of money Lana could have: 17, 18, 19, 20, ...

2. (Refer to the attached image for the table)

A. The table represents the total number of photos and videos on Javier's website based on the number of days since he started the website.

B. The rate of change in the total number of photos on the website each day can be calculated by finding the difference in the number of photos between consecutive days.

The table shows that the number of photos increases by 4 each day. So, the rate of change in the total number of photos is +4.

C. To write a linear equation that shows the relationship between the total number of videos (v) on the website and the number of days (x) since Javier started the website, we can use the given information.

The equation can be written as:
v = x - 12

Explanation:
- On the day Javier started the website, he posted 12 photos and no videos. This is represented by the y-intercept of -12.
- For each day after he started the website, he posts 1 new video. This is represented by the rate of change in the equation, which is +1.