Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two simple inequalities using the words 'and' or 'or'.

Front

What does the symbol '≤' mean in an inequality?

Back

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

Front

What does the symbol '≥' mean in an inequality?

Back

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

Front

When do you use a closed dot on a number line?

Back

A closed dot is used when the inequality includes '≤' or '≥', indicating that the endpoint is included.

Front

When do you use an open dot on a number line?

Back

An open dot is used when the inequality uses '<' or '>', indicating that the endpoint is not included.

Front

How do you graph the inequality -2 ≤ x ≤ 5?

Back

You place a closed dot at -2 and 5, then shade the region between them.

Front

What is the solution set for the inequality -9 < x < 5?

Back

The solution set includes all numbers greater than -9 and less than 5.

Front

What does 'x > 2 or x ≤ -3' mean?

Back

It means that x can be any number greater than 2 or any number less than or equal to -3.

Front

How do you solve the compound inequality -13 < 2x + 5 < 15?

Back

First, isolate 2x by subtracting 5 from all parts: -18 < 2x < 10. Then divide by 2: -9 < x < 5.

Front

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

Back

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