Variable Inequalities Review

Select the correct graph for

y≥7x-3

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Select the correct graph for

y< -⅘(x)+4

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Which point below is NOT a part of the solution set?

• (0, 0)
• (0, 1)
• (-100, -3)
• (5, 10)

Are the points on the boundary line part of the solution set or not?

• Yes, they are part of the solution set
• No, they are NOT part of the solution set
• Some are, and some are not
• There is not enough information to tell

Which system of inequalities matches this graph?

• x≤-2
  y≤x-3
• y≤-2
  y≤x-3
• x≥-2
  y≤x-3
• y≥-2
  y≤x-3

Which system of inequalities matches this graph?

• y≥-2x+3
  y≤x-3
• y>2x+3
  y≥x-3
• y>-2x+3
  y≥x-3
• y<-2x+3
  y≤x-3

Write a system of inequalities to model the following situation:
"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

Write a system of inequalities to model the following situation:
"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 Culver's Restaurant and $25/hour mowing lawns.  He only has time to work 14 hours before homecoming. Which system of inequalities below correctly models Cullin's constraints?

• 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

Which system of inequalities is shown?

• y ≥ -x - 1
  y < x + 4
• y < -x - 1
   y ≥ x + 4
• y > -x - 1
  y ≥ x + 4
• y > -x + 1
  y ≥ x + 4