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

Solve the compound inequality: -2 < x - 9 < 3.

Back

7 < x < 12.

Front

What does the 'and' in a compound inequality signify?

Back

The 'and' signifies that both conditions must be true simultaneously.

Front

What does the 'or' in a compound inequality signify?

Back

The 'or' signifies that at least one of the conditions must be true.

Front

Graph the inequality: x > 2 or x ≤ -3.

Back

The graph shows an open circle at 2 extending to the right and a closed circle at -3 extending to the left.

Front

Write the compound inequality for the graph that shows x ≤ -2 or x > 5.

Back

x ≤ -2 or x > 5.

Front

How do you solve a compound inequality?

Back

Solve each part of the inequality separately and then combine the results.

Front

What is the solution set for the compound inequality: 3 < x < 7?

Back

The solution set is all numbers between 3 and 7, not including 3 and 7.

Front

If x < 4 and x > 1, what is the compound inequality?

Back

1 < x < 4.

Front

What is the graphical representation of x < 5?

Back

An open circle at 5 with a line extending to the left.