2.5 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

How do you solve a compound inequality with 'and'?

Back

To solve a compound inequality with 'and', solve each inequality separately and find the intersection of the solutions.

Front

How do you solve a compound inequality with 'or'?

Back

To solve a compound inequality with 'or', solve each inequality separately and combine the solutions.

Front

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

Back

The solution is -7 < x < 2.

Front

What is the solution to the compound inequality: 3x - 4 < -13 or 7x + 1 > 22?

Back

The solution is x < -3 or x > 3.

Front

How do you graph a compound inequality with 'and'?

Back

Graph the solutions of each inequality on the same number line and shade the region where they overlap.

Front

How do you graph a compound inequality with 'or'?

Back

Graph the solutions of each inequality on the same number line and shade both regions.

Front

What does the notation x ≤ 0 or x ≥ 8 represent?

Back

It represents all values of x that are less than or equal to 0 or greater than or equal to 8.