Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Algebra 1

2.8.5 Practice

Algebra 12.8.5 Practice
Search for key terms or text.

Complete the following questions to practice the skills you have learned in this lesson.

For questions 1 – 2, use the following passage:

A runner is training for a marathon. She runs more than 4 days each week. Each day, she runs between 12 and 15 miles. The marathon is 3 months away at the most.

  1. What does the inequality d > 4 represent?
  1. the number of days the runner runs each week
  2. the number of months away the marathon is
  3. the number of miles the runner runs each day
  4. the number of miles in a marathon
  1. What does the inequality 12 ≤ m ≤ 15 represent?
  1. the number of days the runner runs each week
  2. the number of months away the marathon is
  3. the number of miles the runner runs each day
  4. the number of miles in a marathon

For 3 - 8, write an inequality to represent the constraint given.


  1. There are less than 4 patients, p , in the waiting room.
  1. p ≥ 4
  2. p ≤ 4
  3. p > 4
  4. p < 4

  1. There are no more than 6 cats, c , in the yard.
  1. c ≥ 6
  2. c < 6
  3. c ≤ 6
  4. c > 6

  1. There are no less than 7 markers, m , in the drawer.
  1. m ≥ 7
  2. m < 7
  3. m ≤ 7
  4. m > 7
  1. The basket has between 12 and 19 eggs, e .
  1. 12 ≤ e ≤ 19
  2. e ≤ 19
  3. 12 ≥ e and e ≥ 19
  4. 12 > e and e > 19
  1. The total sales of tickets to a show is more than $68. An adult ticket, a, costs $8 and a children’s ticket, c , is $3.
  1. 8 a + 3 c > 68
  2. 8 a + 3 c < 68
  3. 8 a + 3 c ≥ 68
  4. 8 a + 3 c ≤ 68
  1. There needs to be at least 1 pound of clay, c , for every 4 students, s .
  1. c ≤ s 4
  2. c < s 4
  3. c > s 4
  4. c ≥ s 4

For 9 - 11, use the following passage:

A doctor sees between 7 and 12 patients each day. On Mondays and Tuesdays, the appointment times are 15 minutes. On Wednesdays and Thursdays, they are 30 minutes long. On Fridays, they are one hour long. The doctor works for no more than 8 hours a day. Here are some inequalities that represent this situation.

0.25 ≤ y ≤ 1             7 ≤ x ≤ 12             x y ≤ 8


  1. What does the variable x represent?
  1. the number of patients the doctor sees in a week.
  2. the total time the doctor spends working with patients each day.
  3. the part of an hour that each appointment lasts.
  4. the number of patients the doctor sees each day.

0.25 ≤ y ≤ 1             7 ≤ x ≤ 12             x y ≤ 8


  1. What does the variable y represent?
  1. the number of patients the doctor sees in a week.
  2. the total time the doctor spends working with patients each day.
  3. the part of an hour that each appointment lasts.
  4. the number of patients the doctor sees each day.

0.25 ≤ y ≤ 1             7 ≤ x ≤ 12             x y ≤ 8


  1. What does the expression x y in the last inequality mean in this situation?
  1. the number of patients the doctor sees in a week.
  2. the total time the doctor spends working with patients each day.
  3. the part of an hour that each appointment lasts.
  4. the number of patients the doctor sees each day.

For 12 - 14, use the following passage:

Arnav wants to build a dog house. He makes a list of the materials needed:

  • At least 60 square feet of plywood for the surfaces
  • At least 36 feet of wood planks for the frame of the dog house
  • Between 1 and 2 quarts of paint

Arnav's budget is $65. Plywood costs $0.70 per square foot, planks of wood cost $0.10 per foot, and paint costs $8 per quart.


  1. Which inequality represents the square feet of plywood needed?
  1. 1 ≤ p ≤ 2
  2. p ≥ 36
  3. p ≥ 60

  1. Which inequality represents the number of wood planks needed?
  1. w ≥ 36
  2. 1 ≤ w ≤ 2
  3. w ≥ 60

  1. Which inequality represents the number of quarts of paint needed?
  1. q ≥ 36
  2. 1 ≤ q ≤ 2
  3. q ≥ 60
PreviousNext
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.