Model Inequalities

When graphing an inequality, you use a dotted line when you use which symbol?

• <, >

• ≤, ≥ 

Write the system of inequalities
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

• 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

JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $66 per week? How much does she make?

• b + t < 15
  3b + 6t > 66

• b + t > 15
  3b + 6t < 66

• 3b + 6t > 15
  b + t < 66

• 3b + 6t < 15
  b + t < 66

Which sentence represents m > 41?

• Mary’s points, m, totaled more than 41

• Calvin ran no less than 41 miles, m

• The temperature, m, was less than 41°F

• The magazines’ cost, m, was not more than $41.

Write the system of inequalities
Eiko is drawing caricatures at a fair for 8 hours (480 minutes). She can complete a small drawing in 15 minutes and charges $10 for the drawing. She can complete a larger drawing in 45 minutes and charges $25 for the drawing. Eiko hopes to make at least $200 at the fair. 

• 10x+15y≤480
  45x+25y≥250

• 10x+25y≤200
  15x+45y≤480

• 10x+25y>200
  15x+45y<480

• 10x+25y≥200
  15x+45y≤480

Cullin needs to save at least $100 for homecoming. He works 2 jobs earning $8/hour at Culvers and $25/hour mowing lawns. He only has time to work 14 hours before homecoming.

• x + y  ≥ 25
  x + y ≤ 8

• 100x + 25 y ≤ 100
  2x + 8y ≤ 14

• x + y ≥ 100
  8x + 25y ≤ 14

• 8x + 25y ≥ 100
  x + y ≤ 14

Tyler has no more than $20 in his bank account.

• >

• <

• >

• <

This is a graph of which inequality?

• y > 4x - 2

• y > -2x + 4

• y < -2x

• y < 4X - 2

Which of the following is true of the given graph?

y ≥ -2x + 1

• The graph is a dotted line, shaded above.

• The graph is a solid line, shaded above.

• The graph is a dotted line, shaded below.

• The graph is a solid line, shaded below.

• A dotted line

• A solid line

• Shade up

• Shade down