volume_mute
Product of Two Negative Numbers
publish date: 2026/05/23 08:46:45.665590 UTC
volume_mute
Solve the equation \(7x - 5 = 10x - 11\) by transposing unknowns to the right side. The resulting step requires \(-3x = -6\), which gives \(x = \frac{-6}{-3}\).
What must \((-1) \times (-1)\) equal for the solution to be consistent?
Correct Answer
1
Explanation
When solving \(-3x = -6\), we get \(x = \frac{-6}{-3} = \frac{(-1) \times 6}{(-1) \times 3}\). For the solution to equal 2 (consistent with solving by the other transposition), \((-1)/(-1)\) must equal 1. This algebraically justifies why a negative divided by a negative (or the product of two negatives) yields a positive.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012