Question

PLEASE HELP ANSWER, 35 points!!

Answer 1

A)
`3500\geq248x+1268`

B)

`3500\geq248x+1268`

`-1268`
`-1268`

`2232\geq248x`

÷
`248` ÷
`248`

`9\geq{x}`

C) To graph this equation a number line can be used, this would look something like the "Number Line" attached png, with a closed circle on the right end in order to indicate the family could stay less than or equal to 9 nights within their budget, and the left side has an open end at 0 nights to indicate that they would be staying at least 1 night (since the family is going on vacation we assume they plan to spend at least 1 night at their destination.

Answer 2

The family can stay in the hotel for at most 9 nights.

Explanation:

Part A:

Let x be the number of nights the family can stay in the hotel.

The total cost of the hotel is 248x dollars.

The total cost of the vacation is 248x+1268 dollars.

The family has budgeted to spend $3500 or less, so we can write the following inequality:

248x + 1268 <= 3500

Part B:

To solve the inequality, we can subtract 1268 from both sides:

248x <= 3500 - 1268

248x <= 2232

Then, we can divide both sides by 248 to find the maximum number of nights the family can stay:

x <= 2232 / 248

x <= 9

Therefore, the family can stay in the hotel for at most 9 nights.

Part C:

To graph the solution to the inequality x<=9, we can use the following steps:

Draw a number line.

Place a closed circle at 9 to indicate that 9 is included in the solution.

Shade the region to the left of 9, since all numbers less than or equal to 9 are solutions.