Mastering Multiplication and Division with Inequalities

This video tutorial covers solving inequalities involving multiplication and division by positive and negative numbers. It explains the importance of swapping the inequality sign when multiplying or dividing by a negative number. The video also introduces different notations for describing solution sets, including interval and set notation. Several examples are provided to illustrate these concepts, with a focus on understanding the logic behind the operations and the correct application of notations.

What happens to the inequality sign when you multiply or divide both sides of an inequality by a negative number?

• It becomes undefined

• It swaps direction

• It becomes an equality

• It remains the same

If 1 is less than 2, what happens when you multiply both sides by -1?

• 1 becomes greater than 2

• The inequality swaps direction

• 1 is still less than 2

• The inequality becomes undefined

In the inequality -0.5x ≤ 7.5, what is the solution for x after multiplying both sides by -2?

• x ≤ 15

• x ≤ -15

• x ≥ -15

• x ≥ 15

How is the solution set for x ≥ -15 represented in interval notation?

• (-∞, -15)

• [-15, ∞)

• (-15, ∞)

• (-∞, -15]

What is the solution for x in the inequality 75x ≥ 125?

• x ≤ 3/5

• x ≥ 3/5

• x ≤ 5/3

• x ≥ 5/3

How is the solution set for x ≥ 5/3 represented in interval notation?

• (-∞, 5/3)

• (-∞, 5/3]

• (5/3, ∞)

• [5/3, ∞)

In the inequality x/(-3) > -10/9, what is the solution for x after multiplying both sides by -3?

• x < 10/3

• x > -10/3

• x > 10/3

• x < -10/3

How is the solution set for x < 10/3 represented in interval notation?

• (-∞, 10/3]

• (-∞, 10/3)

• [10/3, ∞)

• (10/3, ∞)

In the inequality x/(-15) < 8, what is the solution for x after multiplying both sides by -15?

• x < 120

• x > 120

• x < -120

• x > -120

How is the solution set for x > -120 represented in interval notation?

• (-120, ∞)

• [-120, ∞)

• (-∞, -120)

• (-∞, -120]