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 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: -4x + 1 ≤ 21 and 5x + 2 < 22?

Back

x ≥ -5 and x < 4.

Front

What is the solution to the compound inequality: 3x + 2 < -4 or 4x + 4 > 24?

Back

x < -2 or x > 5.

Front

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

Back

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

Front

What does the notation 'x < a' represent?

Back

It represents all numbers less than 'a'.

Front

What does the notation 'x > a' represent?

Back

It represents all numbers greater than 'a'.