Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more 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

What does the graph of x > 2 or x ≤ -3 look like?

Back

It shows two separate regions: one to the right of 2 and one to the left of -3.

Front

What is the solution to the inequality -3 ≤ 2x - 1 ≤ 5?

Back

-1 ≤ x ≤ 3.

Front

What does the graph of x ≥ 2 and x ≤ 4 represent?

Back

It represents all values of x between 2 and 4, including 2 and 4.