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', 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 does the inequality -2 < x < 3 represent on a number line?

Back

It represents all numbers between -2 and 3, not including -2 and 3.

Front

How do you graph the inequality x > 2 or x ≤ -3?

Back

Graph a dashed line at x = 2 and shade to the right, then graph a solid line at x = -3 and shade to the left.

Front

What is the solution to the compound inequality -2 < x - 9 < 3?

Back

The solution is 7 < x < 12.

Front

What does the notation x ≤ -2 OR x > 5 mean?

Back

It means that x can be any number less than or equal to -2 or any number greater than 5.

Front

How do you write the compound inequality for the graph that shows x < -1 and x > 3?

Back

The compound inequality is x < -1 or x > 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.

Front

If x < 4 and x > 1, what is the solution set?

Back

The solution set is 1 < x < 4.