Graphing Inequalities and Regions

The video tutorial explains how to set up and solve a problem involving time management for writing and exercising. It introduces variables to represent unknowns, sets up inequalities based on given constraints, and demonstrates how to graph these inequalities. The tutorial emphasizes the importance of shading to identify the feasible region where all conditions are met. The session concludes with a brief overview of the next steps.

What is the total number of hours Ramire has budgeted for writing and exercising each week?

• 50 hours

• 60 hours

• 40 hours

• 30 hours

What is the minimum number of hours Ramire wants to exercise each week?

• 1 hour

• 2 hours

• 3 hours

• 4 hours

What is the maximum number of hours Ramire wants to exercise each week?

• 25 hours

• 15 hours

• 20 hours

• 18 hours

What is the range of hours Ramire hopes to write each week?

• 20 to 25 hours

• 22 to 30 hours

• 30 to 40 hours

• 25 to 35 hours

What variable is used to represent the hours Ramire exercises?

• b

• a

• y

• x

What variable is used to represent the hours Ramire writes?

• a

• y

• x

• b

Which inequality represents the total hours constraint for Ramire's activities?

• x + y ≥ 40

• x + y > 40

• x + y < 40

• x + y ≤ 40

Which inequality represents the minimum exercise hours for Ramire?

• x > 3

• x ≥ 3

• x ≤ 3

• x < 3

Which inequality represents the maximum exercise hours for Ramire?

• x < 18

• x > 18

• x ≤ 18

• x ≥ 18

Which inequality represents the minimum writing hours for Ramire?

• y < 22

• y ≥ 22

• y ≤ 22

• y > 22