Model
Solve and Graph
Write
100
What do you use to model a variable?
A rectangle: red or shaded if -, green or unshaded if +
100
Which number line represents the solution set to x ≠ ?
D
100
Match the inequality symbol for each of the phrases
1. at most
2. over
3. At least
4. maximum
1. ≤
2. >
3. ≥
4. <
200
Miriam is making a bulletin board that is shaped like a square. She has 72 inches of border material. If x represents the length of one side of the bulletin board, which inequality model best represents the possible side lengths of Miriam’s bulletin board?
A.
200
Which number line best represents the solution to the inequality -3x ≥ 14?
- A
- B
- C
- D
B. x ≤ -4.7 (rounded)
200
Which situation is best represented by the inequality 25x ≤ 80?
- A) Angela saves $25 every month. How many months, x, will it take her to save $80 or more?
- B) Marco has 25 songs on his music player. How many additional songs, x, can he put on the music player if it will only hold 80 songs?
- C) Brooke has saved $80 to buy shoes. At DaniCali Shoes, the shoes Brooke wants to buy are $25 per pair. What is the greatest number of pairs of shoes, x, Brooke can buy?
- D) Eighty students will be attending the school play. If each row in the auditorium has 25 chairs, what is the least number of rows, x, that the students will use?
C) Brooke has saved $80 to buy shoes. At DaniCali Shoes, the shoes Brooke wants to buy are $25 per pair. What is the greatest number of pairs of shoes, x, Brooke can buy?
300
Write the inequality for the model below.
3x < 20
300
Jeff needs at least 75 dollars to buy the bicycle he wants. He has earned $32.75 from mowing lawns and has spent $15 on a bicycle helmet. The inequality 75 ≤ m – 15 + 32.75 can be used to find, m, the amount of money he still needs to buy the bicycle. Which number line best represents the solution to the inequality?
- A
- B
- C
- D
D. m ≥ 57.75
300
Which situation can be represented by the inequality ≥ 18?
- A) Ray wants to buy horses. Ray has 18 acres of land, and each horse needs at least
3 acres of land. What is the greatest number of horses Ray can buy? - B) Julie is planting a garden with 3 rows. How many plants does Julie need in order to have at least 18 plants in each row?
- C) Christie uses 3 eggs to make a cake. She has 18 eggs. How many cakes can Christie make if she uses all of her eggs?
- D) Jay wants to run more than 18 miles in 3 days. What is the least number of miles he can run each day to reach his goal?
B) Julie is planting a garden with 3 rows. How many plants does Julie need in order to have at least 18 plants in each row?
400
Which of the following shows a model of the inequality 3x + 2 > -1? (Hint: there can be more than one correct answer)
A and B
400
Which number line represents the solution set for the inequality 8 – 2x < 18 ?
B. x > -5
400
Kathy works at a warehouse packing boxes. Her job is to place p items that each weigh 2 kg into a wooden box that weighs 1 kg. If Kathy can lift a weight of up to 10 kg, which inequality represents the number of items Kathy can place in each box and still be able to lift the box?
- A) p + 2 ≥ 10
- B) p + 2 ≤ 10
- C) 2p + 1 ≥ 10
- D) 2p + 1 ≤ 10
- D) 2p + 1 ≤ 10
500
Which inequality matches the model below.
- A) –3x – 4 ≤ 2
- B) 3x – 4 ≥ –2
- C) –3x – 4 ≥ 2
- D) 3x + 4 ≤ –2
A
500
Which number line represents the solution set to the inequality –1.25x – 3.5 < –3?
A. x > -0.4
500
Which situation can be represented by this inequality –75 + 8.25h ≥ 124.50?
- A) Rich earns $8.25 per hour babysitting. He needs at least $124.50 to attend a basketball game. If he already has $75, how many hours, h, must Rich babysit to afford to go to the basketball game?
- B) Rich earns $8.25 per hour babysitting. He needs at most $124.50 to attend a basketball game. If he already has $75, how many hours, h, must Rich babysit to afford to go to the basketball game?
- C) Rich earns $8.25 per hour babysitting. He needs at least $124.50 to attend a basketball game. If he spends $75 on electronics, how many hours, h, must Rich babysit to afford to go to the basketball game?
- D) Rich earns $8.25 per hour babysitting. He needs at most $75 to attend a basketball game. If he spends $124.50 on electronics, how many hours, h, must Rich babysit to afford to go to the basketball game?
C) Rich earns $8.25 per hour babysitting. He needs at least $124.50 to attend a basketball game. If he spends $75 on electronics, how many hours, h, must Rich babysit to afford to go to the basketball game?