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 notation 'a < x < b' represent?

Back

It represents that x is greater than a and less than b simultaneously.

Front

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

Back

The solution is -8 < r < 3.

Front

How do you graph the solution of a compound inequality?

Back

You graph each part of the inequality on a number line and shade the appropriate regions based on 'and' or 'or'.

Front

What does the inequality x + 8 < 3 represent?

Back

It represents that x is less than -5.

Front

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

Back

The solution is -7 < x < 2.

Front

What does the inequality x > 2 or x ≤ -3 represent on a number line?

Back

It represents two separate regions: all numbers greater than 2 and all numbers less than or equal to -3.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' requires both conditions to be true simultaneously, while 'or' allows for either condition to be true.