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 'and' in a compound inequality signify?

Back

The 'and' signifies that both conditions must be true at the same time.

Front

What does the 'or' in a compound inequality signify?

Back

The 'or' signifies that at least one of the conditions must be true.

Front

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

Back

To solve a compound inequality with 'and', find the intersection of the solution sets of the individual inequalities.

Front

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

Back

To solve a compound inequality with 'or', find the union of the solution sets of the individual inequalities.

Front

What is the solution to the compound inequality 2 < x + 2 < 5?

Back

0 < x < 3.

Front

What is the solution to the compound inequality 0 < x + 7 < 9?

Back

-7 < x < 2.

Front

What is the solution to the compound inequality -4x + 1 ≤ 21 and 5x + 2 < 22?

Back

x ≥ -5 and x < 4.

Front

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

Back

Shade the region where both inequalities overlap on the number line.

Front

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

Back

Shade the regions of both inequalities separately on the number line.