A double inequality like -2 < 3x + 1 < 7 is equivalent to which statement?

A double inequality like -2 < 3x + 1 < 7 is equivalent to which statement?

• A. It represents a single inequality to be solved without splitting
• B. It is equivalent to two separate inequalities that define a range
• C. It cannot be solved
• D. It is always true for all x

Answer: (B)

This kind of double inequality is about handling two bounds at once. For -2 < 3x + 1 < 7, you treat it as two separate conditions: -2 < 3x + 1 and 3x + 1 < 7. Subtracting 1 from each gives -3 < 3x and 3x < 6. Dividing by 3 (a positive number preserves inequality directions) yields -1 < x and x < 2. Putting those together means x must be between -1 and 2, with endpoints excluded because the original inequalities are strict. So this statement is equivalent to two separate inequalities that define a range.

This kind of double inequality is about handling two bounds at once. For -2 < 3x + 1 < 7, you treat it as two separate conditions: -2 < 3x + 1 and 3x + 1 < 7. Subtracting 1 from each gives -3 < 3x and 3x < 6. Dividing by 3 (a positive number preserves inequality directions) yields -1 < x and x < 2. Putting those together means x must be between -1 and 2, with endpoints excluded because the original inequalities are strict. So this statement is equivalent to two separate inequalities that define a range.