Understanding Inequalities and Interval Notation

The video tutorial explains how to represent inequalities using graphs and interval notation. It covers two examples: x ≥ -5 and x < 2. For x ≥ -5, a closed circle is used on the graph at -5, with an arrow pointing to the right, and the interval notation is [-5, ∞). For x < 2, an open circle is used at 2, with an arrow pointing to the left, and the interval notation is (-∞, 2). The tutorial emphasizes the use of square brackets for included endpoints and parentheses for excluded endpoints and infinities.

What does the inequality x ≥ -5 mean in terms of the values x can take?

• x is less than -5

• x is greater than -5

• x is greater than or equal to -5

• x is less than or equal to -5

How is the point at x = -5 represented on the graph for x ≥ -5?

• With a triangle

• With a closed circle

• With an open circle

• With a square

In which direction does the arrow point on the graph for x ≥ -5?

• To the left

• To the right

• Upwards

• Downwards

What is the interval notation for x ≥ -5?

• (-∞, -5]

• (-5, ∞)

• (-∞, -5)

• [-5, ∞)

Why do we use a square bracket in the interval notation for x ≥ -5?

• Because -5 is not included

• Because -5 is included

• Because infinity is included

• Because infinity is not included

What does the inequality x < 2 mean in terms of the values x can take?

• x is greater than or equal to 2

• x is less than 2

• x is less than or equal to 2

• x is greater than 2

How is the point at x = 2 represented on the graph for x < 2?

• With a closed circle

• With a square

• With an open circle

• With a triangle

In which direction does the arrow point on the graph for x < 2?

• To the right

• Downwards

• To the left

• Upwards

What is the interval notation for x < 2?

• (-∞, 2)

• (-∞, 2]

• (2, ∞)

• [2, ∞)

Why do we use a round parenthesis in the interval notation for x < 2?

• Because infinity is included

• Because 2 is not included

• Because infinity is not included

• Because 2 is included