1. The solution to an inequality is graphed on the number line.

Question

A number line going from negative 5 to positive 5. A solid circle appears between positive 4 and positive 5. The number line is shaded from the circle to negative 5.
What is another way to represent this solution set?

{x | x < 4.5}
{x | x ≤ 4.5}
{x | x > 4.5}
{x | x ≥ 4.5}

2. Solve.

5x – 10 ≤ 20

(–∞, 2]
(–∞, 2)
(–∞, 6]
(–∞, 6)

3. What is the first step in solving the inequality 2x + 3 ≥ 17?

Divide the left side by 2.
Subtract 3 from both sides.
Change the direction of the inequality.
Change the inequality to >.

4. Mrs. Valdez wanted to determine the number of people, p, she could safely take in her car to the fun run. She determined that p < 5.

Which statement best describes a possible number of people she can take in her car?

Mrs. Valdez can take –2 people because –2 < 5.
Mrs. Valdez can take 2 people because 2 < 5.
Mrs. Valdez can take 3.5 people because 3.5 < 5.
Mrs. Valdez can take 5 people because 5 < 5.

5. Devin is collecting signatures for a petition to open a new park in her town. She needs to collect at least 1,000 signatures before she can schedule a meeting with the mayor. She already has 380 signatures. If each petition page holds 80 signatures, which inequality best shows how many more pages (p) Devin needs?

7 ≤ p
8 ≤ p
8 < p
9 < p

6. A family has $35 to spend on dinner. They spend $18 on entrees. Side dishes are $3 each. What is the greatest number of side dishes they can buy?

4
5
6
7

7. The solution set to 6 + 2n > 12 is n > 3. Which are correct representations of this solution? Select two options.

{n | n < 3}
{n | n ≥ 3}
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5.
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to negative 5.
(3, ∞)

8. Nala can spend no more than $150 per month on gasoline. She has already purchased $60 in gas this month. Which inequality can be used to find the maximum number of fill-ups she can purchase during the rest of the month, assuming each fill-up costs $30?

30n + 60 > 150
30n + 60 < 150
60n + 30 < 150
60n + 30 > 150

9. Cate solved an inequality to find c, the possible number of cats that a shelter can house. She found that c < 28. Which statement best describes a possible solution to Cate’s problem?

The shelter can house 15.6 cats because 15.6 < 28.
The shelter can house –8 cats because –8 < 28.
The shelter can house 17 cats because 17 < 28.
The shelter can house 28 cats because 28 < 28.

10. Xavier can work no more than 40 hours in a week. He has already worked 24 hours this week. What is the maximum number of 8-hour days Xavier can work for the rest of the week?

2
3
4
5

Answer 1

Here are the answers to each question based on the information provided:

1. What is another way to represent this solution set?
   The solid circle indicates that 4.5 is included (because it's shaded towards negative infinity). Therefore, the correct representation is:
   {x | x ≤ 4.5}

2. Solve. 5x – 10 ≤ 20
   Adding 10 to both sides gives us:
   5x ≤ 30
   Dividing by 5 results in:
   x ≤ 6
   So the correct solution is:
   (–∞, 6]

3. What is the first step in solving the inequality 2x + 3 ≥ 17?
   The first step is to isolate the term involving x. Therefore, you would:
   Subtract 3 from both sides.

4. Which statement best describes a possible number of people she can take in her car?
   Since p < 5, the possible number of people must be less than 5:
   Mrs. Valdez can take 2 people because 2 < 5.

5. Which inequality best shows how many more pages (p) Devin needs?
   She needs at least 1,000 signatures, and she currently has 380. She needs another 1,000 - 380 = 620 signatures. Since each page holds 80 signatures, the inequality is:
   \( p \geq 620/80 \) which simplifies to \( p \geq 7.75 \) (implying that she needs at least 8 pages). Hence:
   8 ≤ p

6. What is the greatest number of side dishes they can buy?
   Total money available for side dishes = $35 - $18 = $17. Each side dish costs $3. Therefore, the maximum number of side dishes is:
   17 / 3 = 5.67, so the greatest number of side dishes they can buy is:
   5

7. Which are correct representations of this solution?
   From the solution n > 3, correct representations are:
   A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5.
   and
   (3, ∞)

8. Which inequality can be used to find the maximum number of fill-ups she can purchase during the rest of the month?
   Total gas budget is $150. Already spent is $60, hence:
   \( 30n + 60 ≤ 150 \) or
   \( 30n < 90 \) where \( n \) is the number of fill-ups. Therefore, the correct inequality is:
   30n + 60 < 150

9. Which statement best describes a possible solution to Cate’s problem?
   Since c < 28, we need a number that is less than 28:
   The shelter can house 17 cats because 17 < 28.

10. What is the maximum number of 8-hour days Xavier can work for the rest of the week?
    He can work a maximum of 40 hours. He has already worked 24 hours, so he can work:
    40 - 24 = 16 hours remaining. Each day is 8 hours, so:
    16 / 8 = 2 days. Hence, the maximum number of 8-hour days he can work is:
    2

If you have any further questions or need additional clarification, feel free to ask!