Compound Inequalities & Special Cases

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using 'AND' or 'OR'.

Front

What does 'AND' mean in compound inequalities?

Back

In 'AND' inequalities, the solution must satisfy both conditions simultaneously.

Front

What does 'OR' mean in compound inequalities?

Back

In 'OR' inequalities, the solution can satisfy either condition.

Front

How do you graph 'AND' inequalities?

Back

Shading connects the two endpoints, indicating the overlap of the solutions.

Front

How do you graph 'OR' inequalities?

Back

Shading points away from the endpoints, indicating that solutions can be on either side.

Front

What is the solution to the compound inequality -2 < x < 0?

Back

The solution includes all numbers between -2 and 0, not including -2 and 0.

Front

What is the solution to the compound inequality x < -2 or x ≥ 4?

Back

The solution includes all numbers less than -2 and all numbers greater than or equal to 4.

Front

What does the graph of x > 2 look like?

Back

An open circle at 2 and shading to the right, indicating all numbers greater than 2.

Front

What does the graph of x ≤ -3 look like?

Back

A closed circle at -3 and shading to the left, indicating all numbers less than or equal to -3.

Front

What is the difference between 'x < -2' and 'x ≤ -2'?

Back

'x < -2' does not include -2, while 'x ≤ -2' includes -2.