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

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 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 + 2 < -4?

Back

x < -2.

Front

What is the solution to the inequality 4x + 4 > 24?

Back

x > 5.

Front

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

Back

-8 < r < 3.

Front

How do you graph the inequality x ≤ -2 OR x > 5?

Back

Shade the region to the left of -2 and the region to the right of 5 on a number line.

Front

What is the difference between 'x < 5' and 'x ≤ 5'?

Back

'x < 5' means x can be any number less than 5, while 'x ≤ 5' includes 5 itself.