Graphing Compound Inequalities

Front

What is a compound inequality?

Back

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

Front

What does 'OR' mean in compound inequalities?

Back

'OR' means that at least one of the inequalities must be true for the solution to be valid.

Front

What does 'AND' mean in compound inequalities?

Back

'AND' means that both inequalities must be true for the solution to be valid.

Front

How do you graph 'OR' inequalities?

Back

Graph each inequality separately and shade the regions that satisfy either inequality, which will not overlap.

Front

How do you graph 'AND' inequalities?

Back

Graph each inequality separately and shade the region where both inequalities overlap.

Front

What does a closed circle represent on a number line?

Back

A closed circle indicates that the number is included in the solution (e.g., ≤ or ≥).

Front

What does an open circle represent on a number line?

Back

An open circle indicates that the number is not included in the solution (e.g., < or >).

Front

How do you write the inequality for the graph with a closed circle at -2 and an open circle at 5?

Back

-2 ≤ x < 5.

Front

What is the solution set for x > 2 or x ≤ -3?

Back

The solution set includes all numbers greater than 2 and all numbers less than or equal to -3.

Front

What is the difference between 'x < 4' and 'x ≤ 4'?

Back

'x < 4' does not include 4, while 'x ≤ 4' includes 4.