4.5: Writing Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using 'and' or 'or'. For example, x > 2 and x < 5 is a compound inequality.

Front

What does the symbol '∪' represent in inequalities?

Back

The symbol '∪' represents the union of two sets, meaning that it includes all values from both inequalities.

Front

What does the symbol '∩' represent in inequalities?

Back

The symbol '∩' represents the intersection of two sets, meaning that it includes only the values that satisfy both inequalities.

Front

How do you graph the inequality x < 3?

Back

To graph x < 3, draw a number line, place an open circle at 3, and shade to the left to indicate all numbers less than 3.

Front

What does an open interval (a, b) mean?

Back

An open interval (a, b) includes all numbers between a and b, but not a and b themselves.

Front

What does a closed interval [a, b] mean?

Back

A closed interval [a, b] includes all numbers between a and b, including a and b.

Front

How do you write the inequality for the graph with a closed circle at -1 and an open circle at 4?

Back

The inequality is written as -1 ≤ x < 4.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true (intersection), while 'or' means at least one condition must be true (union).

Front

How do you express the solution to the compound inequality 2 < x < 5?

Back

The solution can be expressed as the interval (2, 5).

Front

What is the inequality represented by the graph with a closed circle at 0 and an open circle at 3?

Back

The inequality is written as 0 ≤ x < 3.