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

What is the solution set for the compound inequality x < 1 and x > 5?

Back

There is no solution because no number can be both less than 1 and greater than 5.

Front

How do you solve the compound inequality -4x + 1 ≤ 21 and 5x + 2 < 22?

Back

First, solve each inequality separately: -4x ≤ 20 (x ≥ -5) and 5x < 20 (x < 4). The solution set is x ≥ -5 and x < 4.

Front

What is the solution set for the compound inequality 5x + 1 < 21 OR 3x + 2 > -1?

Back

The solution set is all real numbers because at least one of the inequalities is always true.

Front

How do you represent the solution set of an inequality on a number line?

Back

Use open circles for non-inclusive endpoints and closed circles for inclusive endpoints, shading the region that satisfies the inequality.

Front

What is the difference between inclusive and exclusive intervals?

Back

Inclusive intervals include the endpoints (e.g., [a, b]), while exclusive intervals do not (e.g., (a, b)).

Front

What is the solution set for the inequality x ≥ 3 and x < 7?

Back

The solution set is [3, 7).

Front

How do you graph the compound inequality x < 2 or x > 5?

Back

Graph two separate regions: one to the left of 2 and one to the right of 5, using open circles at 2 and 5.