Inequalities and Interval Notation

Front

Define interval notation.

Back

Interval notation is a mathematical notation used to represent a range of values on the number line. It uses parentheses and brackets to indicate whether endpoints are included or excluded.

Front

What does the notation \( (a, b) \) represent?

Back

The notation \( (a, b) \) represents an open interval, meaning it includes all real numbers between \( a \) and \( b \), but not the endpoints \( a \) and \( b \).

Front

What does the notation \( [a, b] \) represent?

Back

The notation \( [a, b] \) represents a closed interval, meaning it includes all real numbers between \( a \) and \( b \), including the endpoints \( a \) and \( b \).

Front

What does the notation \( (a, b] \) represent?

Back

The notation \( (a, b] \) represents a half-open interval, meaning it includes all real numbers between \( a \) and \( b \), including \( b \) but not \( a \).

Front

What does the notation \( [a, b) \) represent?

Back

The notation \( [a, b) \) represents a half-open interval, meaning it includes all real numbers between \( a \) and \( b \), including \( a \) but not \( b \).

Front

How do you express 'all real numbers except for 1 and 4' in interval notation?

Back

\( (-\infty, 1) \cup (1, 4) \cup (4, +\infty) \)

Front

What is the interval notation for \( x > 8 \)?

Back

\( (8, +\infty) \)

Front

How do you express 'x > 0 or x ≤ -1' in interval notation?

Back

\( (-\infty, -1] \cup (0, +\infty) \)

Front

What is the interval notation for 'x < 4 or x ≥ 7'?

Back

\( (-\infty, 4) \cup [7, +\infty) \)

Front

How do you express 'x ≥ -6 or x < -9' in interval notation?

Back

\( (-\infty, -9) \cup [-6, +\infty) \)