We can notice that after we multiplied by -2, the side which was greater became smaller and the side which was smaller became greater. This is why we must reverse the inequality sign. However, if we had multiplied by a positive number, the sign would have remained unchanged.
The concept behind both properties is very similar when we want to multiply both sides by a positive number. Doing this does not modify the equation or the inequality. However, when we can multiply by a negative number, an equation is not altered. In the case of an inequality, multiplying by a negative changes everything and makes us reverse the inequality sign.
