Understanding Inequalities and Problem Solving

The video tutorial explains how to set up and solve an inequality problem involving two individuals, Dornisha and Holden, jogging different distances. It begins by defining variables for the miles jogged by each person and formulates an inequality to represent the scenario. The tutorial then demonstrates solving the inequality for one of the variables and provides examples to illustrate when the inequality holds true or false. The video concludes with a summary of the key points discussed.

What does the variable 'd' represent in the problem?

• The total miles both jogged

• The number of miles Holden jogged

• The difference in miles between Dornisha and Holden

• The number of miles Dornisha jogged

Which inequality represents the scenario where Dornisha jogged at least 2.3 more miles than Holden?

• d ≥ h + 2.3

• d = h + 2.3

• d < h + 2.3

• d > h + 2.3

If Dornisha jogged 8.4 miles, what is the inequality to find Holden's miles?

• 8.4 > h + 2.3

• 8.4 = h + 2.3

• 8.4 < h + 2.3

• 8.4 ≥ h + 2.3

What operation is used to isolate 'h' in the inequality 8.4 ≥ h + 2.3?

• Divide both sides by 2.3

• Subtract 2.3 from both sides

• Add 2.3 to both sides

• Multiply both sides by 2.3

What is the simplified inequality for Holden's miles after solving 8.4 ≥ h + 2.3?

• h > 6.1

• h < 6.1

• h ≥ 6.1

• h ≤ 6.1

Which value of 'h' makes the inequality h ≤ 6.1 true?

• 6.2

• 6

• 6.5

• 7

Which value of 'h' makes the inequality h ≤ 6.1 false?

• 5

• 6

• 6.1

• 7

What does it mean if h is greater than 6.1 in the context of this problem?

• Holden jogged less than Dornisha

• Holden jogged more than Dornisha

• Holden jogged 6.1 miles

• Holden jogged exactly the same as Dornisha

If Holden jogged 5 miles, what can be said about Dornisha's jogging distance?

• Dornisha jogged less than 7.3 miles

• Dornisha jogged exactly 7.3 miles

• Dornisha jogged more than 7.3 miles

• Dornisha jogged at least 7.3 miles

What is the purpose of reversing the inequality when solving for 'h'?

• To solve for a different variable

• To make the inequality easier to read

• To ensure the inequality is correct

• To change the direction of the inequality