Understanding Inequalities and Interval Notation

The video tutorial explains how to solve and graph inequalities, emphasizing the importance of reversing the inequality symbol when multiplying or dividing by a negative number. It covers two examples, demonstrating how to isolate the variable, graph the solution, and express it using interval notation. The tutorial also highlights the significance of having the variable on the left side for easier graphing and interval notation representation.

What must you do to the inequality symbol when you multiply or divide both sides of an inequality by a negative number?

• Add a plus sign

• Subtract a minus sign

• Reverse it

• Leave it unchanged

In the first example, what operation is performed to isolate the variable X?

• Multiplication

• Subtraction

• Addition

• Division

How is the inequality -4 < X expressed with the variable on the left side?

• X < -4

• X > -4

• X = -4

• -4 > X

What type of point is used on the number line to indicate that -4 is not included in the interval for X > -4?

• Solid point

• Dashed point

• Closed point

• Open point

What is the interval notation for the inequality X > -4?

• (-4, +∞)

• [-4, +∞)

• (-∞, -4]

• (-∞, -4)

In the second example, what operation is performed to solve the inequality 9 ≤ -3X?

• Addition

• Multiplication

• Subtraction

• Division

What happens to the inequality symbol when dividing by -3 in the second example?

• It is doubled

• It remains the same

• It is reversed

• It is squared

How is the inequality -3 ≥ X expressed with the variable on the left side?

• -3 ≤ X

• X = -3

• X ≤ -3

• X ≥ -3

What type of point is used on the number line to indicate that -3 is included in the interval for X ≤ -3?

• Open point

• Dashed point

• Closed point

• Solid point

What is the interval notation for the inequality X ≤ -3?

• (-3, +∞)

• (-∞, -3)

• [-3, +∞)

• (-∞, -3]