Graphing Inequalities and Their Solutions

The video tutorial explains how to solve a system of inequalities by defining variables and constraints, graphing the inequalities, and analyzing the graph to find the solution. The problem involves a person budgeting time for writing and exercising, with specific constraints on the hours spent on each activity. The tutorial guides through setting up the graph, plotting the inequalities, and interpreting the results to find the feasible region that satisfies all conditions.

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

• Graphing the inequalities

• Shading the graph

• Identifying the variables

• Testing the solution

In the given problem, what activity does Ramir spend his spare time on?

• Writing and painting

• Exercising and cooking

• Writing and exercising

• Reading and writing

How many hours per week does Ramir want to exercise at least?

• 12 hours

• 8 hours

• 10 hours

• 5 hours

What is the maximum number of hours Ramir hopes to write per week?

• 25 hours

• 20 hours

• 23 hours

• 18 hours

Which inequality represents the total time constraint for Ramir's activities?

• x + y < 40

• x + y ≥ 40

• x + y ≤ 40

• x + y = 40

What is the inequality for the minimum hours Ramir wants to exercise?

• x ≥ 5

• x ≤ 5

• x > 5

• x < 5

What is the inequality for the maximum hours Ramir wants to exercise?

• x ≤ 12

• x > 12

• x ≥ 12

• x < 12

What is the inequality for the minimum hours Ramir hopes to write?

• y ≥ 16

• y ≤ 16

• y > 16

• y < 16

What is the inequality for the maximum hours Ramir hopes to write?

• y ≥ 23

• y > 23

• y < 23

• y ≤ 23

What type of line represents the inequality x = 5 on a graph?

• Diagonal line

• Vertical line

• Horizontal line

• Curved line