If a b, circle the expression that is greater:

a (b - c) or a (c - b)

Use the properties of inequalities to explain your choice.

The expression that is greater is a (b - c)

Step-by-step explanation:

a b, this means (by the addition property) that c - c > b - c⇒0 > b - c

so for the product a (b - c) we would have a multiplication of a negative number a and another negative number (b - c). We know that the result of the multiplication of two negative numbers is a positive number.

Therefore, a (b - c) > 0

a b, this means by the addition property that c - b > b - b⇒ c - b > 0

so for a (c - b), we have the negative number a multiplied by the positive number (c - b). We know that the result of the multiplication of a negative number by a positive number is negative.

Therefore a (c - b) < 0

Thus, the expression that is greater is the positive one which is a (b - c)