Solving 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

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

Back

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

Front

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

Back

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

Front

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

Back

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

Front

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

Back

When graphing a compound inequality with 'or', you shade the regions of both inequalities on the number line.

Front

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

Back

When graphing a compound inequality with 'and', you shade only the region where both inequalities overlap on the number line.

Front

What is the solution to the compound inequality 24 > -3r > -9?

Back

The solution is -8 < r < 3.

Front

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

Back

The solution is -7 < x and x < 2.

Front

How do you write an inequality from a graph?

Back

To write an inequality from a graph, identify the shaded region and the endpoints, then express it using inequality symbols.