Understanding Inequalities and Notation

The video tutorial covers inequalities, set notation, and interval notation. It explains how to graph inequalities and represent them using set and interval notation. The tutorial includes examples such as x ≥ -4, x > -4, -5 ≤ x < 3, and 0 < x ≤ 5, demonstrating how to graph these inequalities and express them in different notations.

What is the primary focus of this lesson?

• Studying probability and statistics

• Learning about calculus

• Understanding inequalities, set notation, and interval notation

• Solving quadratic equations

In the inequality x ≥ -4, which of the following is true?

• x is less than -4

• x is less than or equal to -4

• x is greater than -4

• x is greater than or equal to -4

How is the inequality x ≥ -4 represented on a graph?

• Open circle at -4, shading to the right

• Open circle at -4, shading to the left

• Closed circle at -4, shading to the right

• Closed circle at -4, shading to the left

What does a hard bracket in interval notation signify?

• The interval is infinite

• The number is included

• The interval is finite

• The number is not included

In set notation, how is the inequality x ≥ -4 written?

• {x | x ≥ -4}

• {x | x ≤ -4}

• {x | x > -4}

• {x | x < -4}

In the context of inequalities, what does the symbol '≥' mean?

• Greater than

• Less than or equal to

• Greater than or equal to

• Less than

In the inequality x ≥ -4, which of the following is not true?

• x is less than -4

• x is greater than or equal to -4

• x is equal to -4

• x is greater than -4

What does a hard bracket in interval notation indicate?

• The interval is infinite

• The number is not included

• The interval is finite

• The number is included

Which of the following is a correct representation of x ≥ -4 in interval notation?

• [-4, ∞)

• [-4, ∞]

• (-4, ∞)

• (-∞, -4]

What is the graphical representation of x ≥ -4?

• Open circle at -4, shading to the left

• Open circle at -4, shading to the right

• Closed circle at -4, shading to the left

• Closed circle at -4, shading to the right