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 the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you solve the compound inequality x > 2 and x < 5?

Back

The solution is 2 < x < 5, meaning x is between 2 and 5.

Front

How do you solve the compound inequality x < -1 or x > 3?

Back

The solution is x < -1 or x > 3, meaning x is less than -1 or greater than 3.

Front

What is the solution to the inequality |x - 2| > 3?

Back

The solution is x < -1 or x > 5.

Front

What is the solution to the inequality |x| < 4?

Back

The solution is -4 < x < 4.

Front

What does it mean if an absolute value inequality has 'or'?

Back

It means that the solutions are in two separate intervals.

Front

What does it mean if an absolute value inequality has 'and'?

Back

It means that the solutions must satisfy both conditions simultaneously.

Front

What is the solution to the inequality |x| > -1?

Back

The solution is 'All real numbers' because the absolute value is always non-negative.