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

What does 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' means that both conditions must be true at the same time.

Front

What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' means that at least one of the conditions must be true.

Front

How is the compound inequality -2 ≤ x ≤ 3 represented graphically?

Back

It is represented by a solid line between -2 and 3, including the endpoints.

Front

How is the compound inequality x < -2 or x > 3 represented graphically?

Back

It is represented by two separate arrows pointing left from -2 and right from 3, with open circles at -2 and 3.

Front

What is the solution set for the inequality -2 < x < 3?

Back

The solution set includes all numbers greater than -2 and less than 3.

Front

What is the difference between a closed interval and an open interval?

Back

A closed interval includes its endpoints (e.g., [a, b]), while an open interval does not (e.g., (a, b)).

Front

What does the notation x ≤ 5 mean?

Back

It means that x can be any number less than or equal to 5.

Front

What is the graphical representation of the inequality 5 < x ≤ 9?

Back

It is represented by an open circle at 5 and a solid circle at 9, with a line connecting them.

Front

How do you solve the compound inequality 3 < x < 7?

Back

The solution is all numbers between 3 and 7, not including 3 and 7.