Compound Inequalities

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

How do you express the compound inequality -8 ≤ x < 8 in interval notation?

Back

[-8, 8)

Front

What does the notation (a, b) represent in interval notation?

Back

It represents an open interval where 'a' and 'b' are not included.

Front

What does the notation [a, b] represent in interval notation?

Back

It represents a closed interval where 'a' and 'b' are included.

Front

Can you use the brackets [ or ] with infinity in interval notation?

Back

No, you cannot use brackets with infinity; you must use parentheses.

Front

What is the solution to the compound inequality 2 < x + 2 < 5?

Back

0 < x < 3

Front

What does a closed circle on a number line indicate?

Back

It indicates that the endpoint is included in the solution set.

Front

What does an open circle on a number line indicate?

Back

It indicates that the endpoint is not included in the solution set.

Front

How do you solve the compound inequality -9 < x ≤ -4?

Back

The solution is (-9, -4].

Front

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

Back

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