4.5: Graphing Compound Inequalities on a Number Line

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'.

Front

What does the symbol \( \infty \) represent in inequalities?

Back

The symbol \( \infty \) represents infinity, indicating that the values extend indefinitely in the positive or negative direction.

Front

How do you graph the inequality \( (-\infty, -2] \)?

Back

To graph \( (-\infty, -2] \), draw a number line, shade all values to the left of -2, and place a closed dot on -2.

Front

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

Back

The notation \( [a, b) \) means that 'a' is included in the interval (closed), while 'b' is not included (open).

Front

How do you graph the inequality \( [5, \infty) \)?

Back

To graph \( [5, \infty) \), draw a number line, place a closed dot on 5, and shade all values to the right of 5.

Front

What is the difference between \( \cup \) and \( \cap \) in compound inequalities?

Back

The symbol \( \cup \) represents the union of sets (values that satisfy either inequality), while \( \cap \) represents the intersection (values that satisfy both inequalities).

Front

How do you graph the compound inequality \( (-\infty, -2) \cup (5, \infty) \)?

Back

To graph \( (-\infty, -2) \cup (5, \infty) \), shade all values to the left of -2 (open dot) and all values to the right of 5 (open dot).

Front

What does the notation \( (-\infty, -2) \) indicate?

Back

The notation \( (-\infty, -2) \) indicates all real numbers less than -2, not including -2.

Front

How do you represent the inequality \( x \leq -2 \) on a number line?

Back

To represent \( x \leq -2 \), draw a number line, place a closed dot on -2, and shade to the left.

Front

What is the graph of the inequality \( x < 5 \)?

Back

To graph \( x < 5 \), draw a number line, place an open dot on 5, and shade to the left.