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

What does 'AND' mean in a compound inequality?

Back

'AND' means that both conditions must be true at the same time for a solution to be valid.

Front

What does 'OR' mean in a compound inequality?

Back

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

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 inequality: 3x - 4 < -13?

Back

x < -3.

Front

What is the solution to the inequality: 7x + 1 > 22?

Back

x > 3.

Front

Solve the compound inequality: 24 > -3r > -9.

Back

-8 < r < 3.

Front

What is the solution to the compound inequality: 3x + 2 < -4 or 4x + 4 > 24?

Back

x < -2 or x > 5.

Front

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

Back

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