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 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' means that both conditions must be true at the same time.

Front

What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' means that at least one of the conditions must be true.

Front

How do you graph a compound inequality with 'and'?

Back

To graph a compound inequality with 'and', find the overlap of the two inequalities on a number line.

Front

How do you graph a compound inequality with 'or'?

Back

To graph a compound inequality with 'or', graph both inequalities separately and shade all regions that satisfy either inequality.

Front

What is the solution to the compound inequality -2 ≤ x ≤ 5?

Back

The solution includes all numbers between -2 and 5, including -2 and 5.

Front

What is the solution to the compound inequality x ≤ -2 OR x > 5?

Back

The solution includes all numbers less than or equal to -2 and all numbers greater than 5.

Front

How do you solve the inequality 3d - 4 < -7 OR 5d + 2 > 12?

Back

First, solve each inequality separately: 3d < -3 (d < -1) and 5d > 10 (d > 2). The solution is d < -1 OR d > 2.

Front

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

Back

'≤' means less than or equal to, while '<' means strictly less than.

Front

What is the difference between '≥' and '>'?

Back

'≥' means greater than or equal to, while '>' means strictly greater than.