Solving and graphing a linear inequality word problem

The video tutorial explains how to solve a system of inequalities by defining variables for exercise and writing hours, formulating inequalities based on given conditions, and graphing these inequalities. The process includes determining the appropriate shading for the solution region on the graph. The tutorial emphasizes understanding the relationships between variables and the importance of testing points to verify solutions.

What is the first step in solving a system of inequalities?

• Identifying the variables

• Testing a point

• Shading the graph

• Graphing the inequalities

What is the maximum number of hours Remir can exercise per week?

• 23 hours

• 16 hours

• 5 hours

• 12 hours

Which inequality represents the total hours Remir can spend on writing and exercising?

• X + Y = 40

• X + Y ≤ 40

• X + Y ≥ 40

• X + Y < 40

What is the range of hours Remir hopes to write per week?

• 5 to 23 hours

• 12 to 16 hours

• 16 to 23 hours

• 5 to 12 hours

What type of line is used to graph the inequality X = 5?

• Curved line

• Horizontal line

• Vertical line

• Diagonal line

How do you determine the shading area for an inequality?

• By using a test point

• By drawing a line

• By calculating the slope

• By finding the intercept

What does the feasible region on the graph represent?

• No solutions

• All possible solutions

• Only one solution

• Infinite solutions

What is the significance of the intersection of shaded regions?

• It shows the maximum value

• It represents the minimum value

• It indicates the feasible solutions

• It is irrelevant

What is the purpose of drawing arrows on the graph?

• To indicate the direction of shading

• To mark the intercepts

• To show the slope

• To highlight the axes

What does the solution set of the system of inequalities indicate?

• The hours he must spend

• The hours he cannot spend

• The range of possible hours for activities

• The exact hours Remir will spend