Understanding Compound Inequalities

This video tutorial by Mr. J covers solving compound inequalities, focusing on both 'or' and 'and' types. It includes four examples, two for each type, demonstrating step-by-step solutions. The video explains how to isolate variables and apply inverse operations, emphasizing the importance of maintaining balance in inequalities. It also highlights the difference in solutions for 'or' and 'and' inequalities, where 'or' requires only one condition to be true, while 'and' requires both.

What is the main difference between 'or' and 'and' compound inequalities?

• 'Or' requires only one condition to be true, 'and' requires both.

• 'Or' and 'and' both require both conditions to be true.

• 'Or' and 'and' both require only one condition to be true.

• 'Or' requires both conditions to be true, 'and' requires only one.

In the inequality 6Y < 30, what operation is used to isolate Y?

• Addition

• Subtraction

• Multiplication

• Division

What is the solution for Y in the inequality 4Y + 10 > 54?

• Y < 11

• Y > 11

• Y > 5

• Y < 5

How does the inequality symbol change when both sides are divided by a negative number?

• It becomes an equal sign.

• It remains the same.

• It becomes a greater than sign.

• It flips direction.

What is the solution for X in the inequality X + 5 < 3?

• X < -2

• X > 2

• X > -2

• X < 2

In an 'and' compound inequality, what must be true for a solution to be valid?

• Only one inequality must be true.

• Both inequalities must be true.

• Neither inequality must be true.

• At least one inequality must be false.

What is the solution for X in the inequality X - 6 ≤ 11?

• X ≤ 5

• X ≤ 17

• X ≥ 5

• X ≥ 17

How do you solve the inequality 3M + 7 < 13?

• Add 7 to both sides.

• Subtract 7 from both sides.

• Divide both sides by 3.

• Multiply both sides by 3.

What is the solution for M in the inequality 3M + 7 ≥ -2?

• M ≥ -3

• M ≤ 3

• M ≥ 3

• M ≤ -3

What is the final solution for M in the compound inequality -3 ≤ M < 2?

• M is greater than or equal to -3 and less than 2.

• M is less than or equal to -3 and greater than 2.

• M is greater than or equal to 2 and less than -3.

• M is less than or equal to 2 and greater than -3.