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', find the intersection of the solution sets of the individual inequalities.

Front

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

Back

To solve a compound inequality with 'or', find the union of the solution sets of the individual inequalities.

Front

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

Back

The solution is -1 ≤ x ≤ 3.

Front

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

Back

The solution is -7 < x < 2.

Front

How do you graph the inequality x > 2 or x ≤ -3?

Back

Graph two separate regions: one for x > 2 (open circle at 2, shading to the right) and one for x ≤ -3 (closed circle at -3, shading to the left).

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the endpoints, while a non-strict inequality (≤ or ≥) includes the endpoints.

Front

What is the graphical representation of the inequality x ≤ -2 or x > 5?

Back

Graph two separate regions: one for x ≤ -2 (closed circle at -2, shading to the left) and one for x > 5 (open circle at 5, shading to the right).