Solving and Graphing 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 the compound inequality 0 < x + 7 < 9?

Back

Subtract 7 from all parts: -7 < x < 2.

Front

What happens to the inequality when you multiply or divide by a negative number?

Back

You must flip the inequality sign.

Front

Is x = 3 a solution to the inequality 6 < x + 5 ≤ 11?

Back

Yes, because 6 < 8 ≤ 11 is true.

Front

What is the solution set for the inequality 2 ≤ x ≤ 4?

Back

The solution set includes all numbers between 2 and 4, including 2 and 4.

Front

What is the solution set for the inequality x > 2 or x ≤ -3?

Back

The solution set includes all numbers greater than 2 and all numbers less than or equal to -3.

Front

How do you graph the inequality x > 2?

Back

Draw a number line, place an open circle at 2, and shade to the right.

Front

How do you graph the inequality 2 ≤ x ≤ 4?

Back

Draw a number line, place closed circles at 2 and 4, and shade between them.