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 the 'and' in a compound inequality signify?

Back

The 'and' signifies that both conditions must be true at the same time.

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

When solving inequalities, what must you do when multiplying or dividing by a negative number?

Back

You must flip the inequality sign.

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 x ≤ -3?

Back

Draw a number line, place a closed circle at -3, and shade to the left.

Front

What is the solution set for the compound inequality -3 ≤ 2x - 1 ≤ 5?

Back

The solution set is -1 ≤ x ≤ 3.

Front

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

Back

The solution set is -8 < r < 3.

Front

How do you solve the compound inequality 2 < x + 3 < 5?

Back

Subtract 3 from all parts: -1 < x < 2.

Front

What is the graphical representation of the inequality x < 4?

Back

Draw a number line, place an open circle at 4, and shade to the left.