A statement like -c<ax+b<c is an example of a double inequality.

A statement like -c<ax+b<c is an example of a double inequality.

• A. Double Inequality
• B. Absolute Inequality
• C. Compound Inequality
• D. Inequation

Answer: (A)

A double inequality is a statement that a quantity lies between two values, expressed with two inequality signs in a row. Here, ax + b is constrained to be between -c and c, which is written as -c < ax + b < c. This single statement captures two comparisons at once: ax + b must be greater than -c and also less than c simultaneously. That simultaneous range is the hallmark of a double inequality. This isn’t an absolute inequality, which would involve absolute value bars like |ax + b| < c. It’s also a specific instance of a compound (chained) inequality, but the standard name for this kind of three-part, two-sign form is a double inequality.

A double inequality is a statement that a quantity lies between two values, expressed with two inequality signs in a row. Here, ax + b is constrained to be between -c and c, which is written as -c < ax + b < c. This single statement captures two comparisons at once: ax + b must be greater than -c and also less than c simultaneously. That simultaneous range is the hallmark of a double inequality.

This isn’t an absolute inequality, which would involve absolute value bars like |ax + b| < c. It’s also a specific instance of a compound (chained) inequality, but the standard name for this kind of three-part, two-sign form is a double inequality.