Understanding Intervals and Inequalities

This video tutorial explains how to express intervals using inequalities and interval notation. It covers examples of closed and open intervals, compound inequalities, and multiple intervals. The tutorial emphasizes the importance of notation order and the use of square brackets and rounded parentheses to indicate inclusion or exclusion of endpoints.

What does a closed point on a number in an interval indicate?

• The number is included in the interval.

• The interval is infinite.

• The number is not included in the interval.

• The interval is undefined.

How is an interval that includes -3 and extends to infinity expressed in interval notation?

• (-3, ∞)

• [-3, ∞]

• [-3, ∞)

• (-3, ∞]

What does an open point on a number in an interval signify?

• The number is not included in the interval.

• The number is included in the interval.

• The interval is undefined.

• The interval is finite.

How would you express an interval that starts at +1 with an open point and moves to negative infinity using inequalities?

• X > 1

• X ≤ 1

• X ≥ 1

• X < 1

In a compound inequality, what does the 'and' connector imply?

• Both conditions must be true simultaneously.

• The conditions are unrelated.

• At least one condition must be true.

• Neither condition can be true.

How is the interval from -5 to 4, where -5 is not included and 4 is included, expressed in interval notation?

• [-5, 4)

• (-5, 4]

• [-5, 4]

• (-5, 4)

What does the 'U' symbol represent in interval notation?

• Union of intervals

• Intersection of intervals

• Difference of intervals

• Complement of intervals

How would you express the interval from -3 to negative infinity using inequalities?

• X ≤ -3

• X > -3

• X ≥ -3

• X < -3

Which interval notation represents an interval from -1 to positive infinity, excluding -1?

• [-1, ∞]

• (-1, ∞]

• [-1, ∞)

• (-1, ∞)

What is the correct interval notation for two separate intervals: one from negative infinity to -3 (including -3) and another from -1 to positive infinity (excluding -1)?

• (-∞, -3) U [-1, ∞)

• (-∞, -3) U (-1, ∞)

• (-∞, -3] U (-1, ∞)

• (-∞, -3] U [-1, ∞)