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 ≥ 2 and x ≤ 4' represent on a number line?

Back

It represents all numbers x that are greater than or equal to 2 and less than or equal to 4, including the endpoints.

Front

How do you graph the inequality 'x < -2 or x > 5'?

Back

You graph two separate regions: one to the left of -2 (not including -2) and one to the right of 5 (not including 5).

Front

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

Back

'And' means both conditions must be true at the same time, while 'or' means at least one of the conditions must be true.

Front

Solve the compound inequality: -3 < 3x < 6. What is the solution?

Back

The solution is -1 < x < 2.

Front

What does the graph of 'x > 2 or x ≤ -3' look like?

Back

It has an open circle at 2 with a line extending to the right, and a closed circle at -3 with a line extending to the left.

Front

What is the solution set for the inequality 'x ≥ 2 and x ≤ 4'?

Back

The solution set is the interval [2, 4].

Front

How do you write a compound inequality for the graph that shows all numbers between -2 and 5, including -2 but not 5?

Back

The compound inequality is -2 ≤ x < 5.

Front

What is the meaning 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.

Front

How do you solve 'x < 4 or x > 6'?

Back

The solution includes all numbers less than 4 and all numbers greater than 6.