Which statement best defines a compound inequality?

Which statement best defines a compound inequality?

• A. A single inequality with two variables
• B. Two inequalities joined by "and" or "or"
• C. An equation and an inequality combined
• D. A pair of equations joined with a comma

Answer: (B)

A compound inequality is formed when two simple inequalities are connected by and or or. It describes a set of values that must satisfy both conditions at once if it’s connected by and, or at least one of the conditions if it’s connected by or. Think of and as narrowing to the overlapping part: you want values that meet both requirements. For example, 2 < x and x ≤ 5 means x is between 2 and 5, exclusively on the left and inclusively on the right—the interval (2, 5]. Think of or as taking the union of two ranges: you want values that meet either condition, such as x < -3 or x > 4, which covers all numbers left of -3 and right of 4. This idea is different from a single inequality with two variables, or from combining an equation with an inequality. The defining feature is two inequalities tied together by and or or.

A compound inequality is formed when two simple inequalities are connected by and or or. It describes a set of values that must satisfy both conditions at once if it’s connected by and, or at least one of the conditions if it’s connected by or.

Think of and as narrowing to the overlapping part: you want values that meet both requirements. For example, 2 < x and x ≤ 5 means x is between 2 and 5, exclusively on the left and inclusively on the right—the interval (2, 5]. Think of or as taking the union of two ranges: you want values that meet either condition, such as x < -3 or x > 4, which covers all numbers left of -3 and right of 4.

This idea is different from a single inequality with two variables, or from combining an equation with an inequality. The defining feature is two inequalities tied together by and or or.