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Algebra 1

2.8.5 Practice

Algebra 12.8.5 Practice

2.8.5 Practice

2.8.5 • Practice

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

For questions 1 – 2, use the following scenario:

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 questions 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 questions 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
  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
  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 questions 12 – 14, use the following scenario:

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
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