Graphing 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 'x ≥ 0' mean?

Back

It means that x is greater than or equal to 0.

Front

What does 'x < 5' mean?

Back

It means that x is less than 5.

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.

Front

How do you graph the inequality '0 ≤ x < 5'?

Back

You would shade the number line starting from 0 (including 0) to 5 (not including 5).

Front

What does the compound inequality 'x > 2 or x ≤ -3' represent on a number line?

Back

It represents all values greater than 2 and all values less than or equal to -3.

Front

How do you interpret 'x < 3 or x ≥ 6'?

Back

It means x can be any value less than 3 or any value greater than or equal to 6.

Front

What does '0 ≥ x ≥ 5' imply?

Back

It implies that x is between 0 and 5, including both endpoints.

Front

How do you solve the compound inequality 'x < 3 and x ≤ 6'?

Back

Since x < 3 is more restrictive, the solution is simply x < 3.

Front

What is the graphical representation of 'x > 2 and x < -3'?

Back

This compound inequality has no solution because no number can be greater than 2 and less than -3 at the same time.