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 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' indicates that both conditions must be true simultaneously.

Front

What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' indicates 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 inequality: 3x + 2 < -4?

Back

x < -2.

Front

What is the solution to the inequality: 4x + 4 > 24?

Back

x > 5.

Front

What is the solution to the compound inequality: -4x + 1 ≤ 21 and 5x + 2 < 22?

Back

x ≥ -5 and x < 4.

Front

What is the solution to the compound inequality: -8 < 2(x + 4) or -3x + 4 > x - 4?

Back

x < -8 or x < 2.

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.