Chapter 1 - Expressions, Equations, and Inequalities - 1-5 Solving Inequalities - Lesson Check - Page 37: 6

See example

We know that $6>2$. Multiplying both sides by $-1$, without reversing signs gives $-6>-2$, which is not true. Let's divide both sides by $-2$, without reversing signs, we get $-3>-1$, which is also not true. Thus, we should reverse signs of the inequality when multiplying or dividing with a negative number because negative numbers “flip” the order on the number line.