Unit 2 Part 1 Two-Step Equations and Inequalities

Adelynn & Henley are helping Mrs Pham pack up library books for the summer. The truck that is taking the books has a total weight limit of 1,400 pounds, and they have already loaded computers that total 200 pounds. They are putting 30 pounds worth of books in the boxes before they load them on the truck. Which inequality represents all of the possible values of x, the number of full boxes that can be loaded on the truck?

• 200x + 30 ≥ 1,400

• 30x + 200 ≥ 1,400

• 200x + 30 ≤ 1,400

• 30x + 200 ≤ 1,400

Isaiah and Lamundre need 2,000 signatures in order to pass a recycling bill. They have collected 750 signatures so far, and there are 5 weeks remaining to collect signatures. Which number line represents the number of signatures the group needs to collect each week?

• F

• G

• H

• J

Emily has 14 apples and she gives away 3 apples to each friend (Addie, Jazzy, Roslynn). How many friends can she give apples to if she wants to keep more than 2 apples for herself? 14- 3f > 2

• f > 4

• f < 4

• f > -4

• f < -4

Which situation could be represented by this equation? 345 + 23x = 677

• Ava is reading a book with 345 pages total. If she reads 23 pages a day for x days, she will have 677 left to read.

• Joneer is reading a book with 677 pages total. If she has already read 345 and plans to read 23 pages a day, how many days, x, will she need to read at that pace until she finishes the entire book?

• Yara has $345 in her bank account. If she withdraws $677, how many days, x, remain until she has $23 left?

• Abigail has $677 in her bank account.If she withdraws $23 a day, how many days, x, remain until she has $345 left?

Keziah is planning a party and has a budget constraint. She needs to choose from a set of items priced at {-10, -6, -2, 2, 4} dollars. Which prices satisfy the condition that -1/2x + 5 ≤ 7

(solve for x. only 1 correct answer)

• -10, -6, and -2 only

• 2 and 4 only

• -2, 2, and 4 only

• All of the values in the set satisfy the inequality.

Sophia and her 3 friends (Lorelei, Lauren, and Gianna) went to an amusement park. They bought their tickets online. At the park, they spent $109.99 throughout the day for food and souvenirs. The total cost of the trip, was $347.95. Which equation represents the total cost?

• 4t + 109.99 = 347.95

• 4 + 109.99t = 347.95

• 4(t + 109.99) = 347.95

• 4(4 + 109.99t) = 347.95

Which situation can be represented by this inequality? 35 ≥ 3.50 + 2.50x

• Aleen can spend at least $35. She has already spent $2.50. How many items, x, worth $3.50 can she purchase?

• Stella can spend at least $35. She has already spent $3.50. How many items, x, worth $2.50 can she purchase?

• Anderson has $35 to spend. He has already spent $2.50. How many items, x, worth $3.50 can he purchase?

• Yusuf has $35 to spend. He already has spent 3.50. How many items, x, worth $2.50 can he purchase?

Irfan is saving money to buy a bicycle. He has already saved $300 and plans to save $250 each month. Which number line represents the solution to the inequality 250x + 300 ≥ 1,550 to find out how many months he needs to save to reach her goal?

• F

• G

• H

• J

Charlie is planning an end of season Volleyball party at the ice rink. The rink charges $80 to rent the location plus 12.50 per guest. Charlie does not want to exceed a budget of $200. What is the maximum number of guests she can invite?

• 8 guests

• 9 guests

• 10 guests

• 11 guests

Blake is buying b packs of pencils, each costing $2. Which equation is true when b = 2?

• 12 + 3b = -24

• 9 - 6b = 3

• 4(b + 3) = 20

• 22 - 2b = 15