Solving Inequalities and Compound Inequalities

In this video, Mr. J explains how to solve compound inequalities involving 'or'. He demonstrates solving two separate inequalities: 6Y < 30 and 4Y + 10 > 54. For each inequality, he isolates the variable Y by performing inverse operations. After solving both inequalities, he combines them into a compound inequality: Y < 5 or Y > 11. Mr. J emphasizes that a solution exists if either inequality is true, meaning Y can be any number less than 5 or greater than 11. The video concludes with a recap of the process.

What is the first step in solving a compound inequality involving 'or'?

• Solve each inequality separately.

• Multiply the inequalities.

• Solve both inequalities together.

• Add the inequalities.

What operation is used to isolate Y in the inequality 6Y < 30?

• Multiplication

• Subtraction

• Division

• Addition

After dividing both sides of 6Y < 30 by 6, what is the resulting inequality?

• Y > 6

• Y < 6

• Y > 5

• Y < 5

What is the first step to solve the inequality 4Y + 10 > 54?

• Multiply both sides by 4.

• Divide both sides by 4.

• Subtract 10 from both sides.

• Add 10 to both sides.

What is the result of subtracting 10 from both sides of 4Y + 10 > 54?

• 4Y < 44

• 4Y > 44

• 4Y > 64

• 4Y < 64

What operation is used to isolate Y in the inequality 4Y > 44?

• Addition

• Subtraction

• Multiplication

• Division

What is the resulting inequality after dividing both sides of 4Y > 44 by 4?

• Y > 10

• Y > 11

• Y < 11

• Y < 10

How do you express the solution of the compound inequality involving 'or'?

• Y is greater than 5 or less than 11

• Y is less than 5 and greater than 11

• Y is less than 5 or greater than 11

• Y is greater than 5 and less than 11

What does it mean for a compound inequality involving 'or' to be true?

• The inequalities must be equal.

• Both inequalities must be true.

• Neither inequality can be true.

• At least one inequality must be true.

Which of the following is a solution to the compound inequality Y < 5 or Y > 11?

• Y = 11

• Y = 4

• Y = 10

• Y = 6