Inequalities and Systems of Inequalities

How can I tell if an inequality will have a solid line?

• It has an equal sign.

• The symbol is greater than.

• The symbol has "or equal to."

• You just guess.

Which point below is NOT part of the solution set?

• (0, 0)

• (-10, -10)

• (-1, 5)

• (5, 20)

Gabriela is the manager of a print shop. She needs to schedule employees to work no more than 300 person-hours per week. She has one 20 hour a week part-time employee. Each full-time employee works 40 hours per week. Which inequality will determine f, the number of full-time employees Gabriela can schedule to remain under the 300 person-hour per week limit?

Which inequality describes the graph?

Which inequality describes the graph?

Which inequality describes the graph?

Which system of inequalities describes the graph?

Cody’s Gym charges a $15 fee to join and $30 per month. Tyler’s Gym charges a $30 fee to join and $20 per month. Write an inequality that could be used to determine after how many months Tyler’s gym would be a better deal.

• 30 + 20x < 15 + 30x

• 30x + 20 < 15x + 30

• 30 + 20x > 15 + 30x

• 30x + 20 > 15x + 30

Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing. Which systems of inequalities represents this situation?

• x+y≤300

  
  

  7.5x+5.5y≥2000

• x+y<300

  
  

  7.5x+5.5y≥2000

• x+y≤300

  
  

  7.5x+5.5y≤2000

• x+y>2000

  
  

  7.5x+5.5y≤300

You can work at most 20 hours next week. You need to earn at least $92 to cover you weekly expenses. Your math tutoring job pays $7.50 per hour and your job as a pet sitter pays $6 per hour. You can work at most 7 hours tutoring. Which system of linear inequalities to models the situation?

• s + t < 20

  
  

  6s + 7.50t ≥ 92

  
  

  t >7

• s + t ≤ 20

  
  

  6s + 7.50t ≥ 92

  
  

  t ≤ 7